WASHINGTON AND NEW YORK (Reuters) - In September 2001, as the U.S. reeled from the terrorist attacks on the World Trade Center and the Pentagon, Vladimir Putin supported Washington's imminent invasion of Afghanistan in ways that would have been inconceivable during the Cold War.

He agreed that U.S. planes carrying humanitarian aid could fly through Russian air space. He said the U.S. military could use airbases in former Soviet republics in Central Asia. And he ordered his generals to brief their U.S. counterparts on their own ill-fated 1980s occupation of Afghanistan.

During Putin's visit to President George W. Bush's Texas ranch two months later, the U.S. leader, speaking at a local high school, declared his Russian counterpart "a new style of leader, a reformer…, a man who's going to make a huge difference in making the world more peaceful, by working closely with the United States."

For a moment, it seemed, the distrust and antipathy of the Cold War were fading.

Then, just weeks later, Bush announced that the United States was withdrawing from the Anti-Ballistic Missile Treaty, so that it could build a system in Eastern Europe to protect NATO allies and U.S. bases from Iranian missile attack. In a nationally televised address, Putin warned that the move would undermine arms control and nonproliferation efforts.

"This step has not come as a surprise to us," Putin said. "But we believe this decision to be mistaken."

The sequence of events early in Washington's relationship with Putin reflects a dynamic that has persisted through the ensuing 14 years and the current crisis in Ukraine: U.S. actions, some intentional and some not, sparking an overreaction from an aggrieved Putin.

As Russia masses tens of thousands of troops along the Russian-Ukrainian border, Putin is thwarting what the Kremlin says is an American plot to surround Russia with hostile neighbors. Experts said he is also promoting "Putinism" - a conservative, ultra-nationalist form of state capitalism - as a global alternative to Western democracy.

NOT PAYING ATTENTION?

It's also a dynamic that some current and former U.S. officials said reflects an American failure to recognize that while the Soviet Union is gone as an ideological enemy, Russia has remained a major power that demands the same level of foreign policy attention as China and other large nations - a relationship that should not just be a means to other ends, but an end in itself.

"I just don't think we were really paying attention," said James F. Collins, who served as the U.S. ambassador to Moscow in the late 1990s. The bilateral relationship "was seen as not a big deal."

Putin was never going to be an easy partner. He is a Russian nationalist with authoritarian tendencies who, like his Russian predecessors for centuries, harbors a deep distrust of the West, according to senior U.S. officials. Much of his world view was formed as a KGB officer in the twilight years of the Cold War and as a government official in the chaotic post-Soviet Russia of the 1990s, which Putin and many other Russians view as a period when the United States repeatedly took advantage of Russian weakness.

Since becoming Russia's president in 2000, Putin has made restoring Russia's strength - and its traditional sphere of influence - his central goal. He has also cemented his hold on power, systematically quashed dissent and used Russia's energy supplies as an economic billy club against its neighbors. Aided by high oil prices and Russia's United Nations Security Council veto, Putin has perfected the art of needling American presidents, at times obstructing U.S. policies.

Officials from the administrations of Presidents Bush and Barack Obama said American officials initially overestimated their potential areas of cooperation with Putin. Then, through a combination of overconfidence, inattention and occasional clumsiness, Washington contributed to a deep spiral in relations with Moscow.

COMMON CAUSE

Bush and Putin's post-2001 camaraderie foundered on a core dispute: Russia's relationship with its neighbors. In November 2002, Bush backed NATO's invitation to seven nations - including former Soviet republics Estonia, Latvia and Lithuania - to begin talks to join the Western alliance. In 2004, with Bush as a driving force, the seven Eastern European nations joined NATO.

Putin and other Russian officials asked why NATO continued to grow when the enemy it was created to fight, the Soviet Union, had ceased to exist. And they asked what NATO expansion would do to counter new dangers, such as terrorism and proliferation.

"This purely mechanical expansion does not let us face the current threats," Putin said, "and cannot allow us to prevent such things as the terrorist attacks in Madrid or restore stability in Afghanistan."

Thomas E. Graham, who served as Bush's senior director for Russia on the National Security Council, said a larger effort should have been made to create a new post-Soviet, European security structure that replaced NATO and included Russia.

"What we should have been aiming for - and what we should be aiming for at this point," Graham said, "is a security structure that's based on three pillars: the United States, a more or less unified Europe, and Russia."

Graham said small, incremental attempts to test Russian intentions in the early 2000s in Afghanistan, for example, would have been low-risk ways to gauge Putin's sincerity. "We never tested Putin," Graham said. "Our policy never tested Putin to see whether he was really committed to a different type of relationship."

But Vice President Dick Cheney, Senator John McCain and other conservatives, as well as hawkish Democrats, remained suspicious of Russia and eager to expand NATO. They argued that Moscow should not be given veto power over which nations could join the alliance, and that no American president should rebuff demands from Eastern European nations to escape Russian dominance.

DEMOCRACY IN OUR TIME

Another core dispute between Bush and Putin related to democracy. What Bush and other American officials saw as democracy spreading across the former Soviet bloc, Putin saw as pro-American regime change.

The 2003 U.S. invasion of Iraq, without U.N. authorization and over the objections of France, Germany and Russia, was a turning point for Putin. He said the war made a mockery of American claims of promoting democracy abroad and upholding international law.

Putin was also deeply skeptical of U.S. efforts to nurture democracy in the former Soviet bloc, where the State Department and American nonprofit groups provided training and funds to local civil-society groups. In public speeches, he accused the United States of meddling.

In late 2003, street protests in the former Soviet republic of Georgia, known as the Rose Revolution, led to the election of a pro-Western leader. Four months later, street protests in Ukraine that became known as the Orange Revolution resulted in a pro-Western president taking office there.

Putin saw both developments as American-backed plots and slaps in the face, so soon after his assistance in Afghanistan, according to senior U.S. officials.

In 2006, Bush and Putin's sparring over democracy intensified. In a press conference at the first G-8 summit hosted by Russia, the two presidents had a testy exchange. Bush said that the United States was promoting freedom in Iraq, which was engulfed in violence. Putin openly mocked him.

"We certainly would not want to have the same kind of democracy as they have in Iraq," Putin said, smiling as the audience erupted into laughter, "I will tell you quite honestly."

Bush tried to laugh off the remark. "Just wait," he replied, referring to Iraq.

A PITSTOP IN MOSCOW?

Graham said the Bush administration telegraphed in small but telling ways that other foreign countries, particularly Iraq, took precedence over the bilateral relationship with Moscow.

In 2006, for example, the White House asked the Kremlin for permission for Bush to make a refueling stop in Moscow on his way to an Asia-Pacific summit meeting. But it made clear that Bush was not looking to meet with Putin, whom he would see on the sidelines of the summit.

After Russian diplomats complained, Graham was sent to Moscow to determine if Putin really wanted a meeting and to make clear that if there was one, it would be substance-free.

In the end, the two presidents met and agreed to ask their underlings to work on a nonproliferation package.

"When the Russian team came to Washington in December 2006, in a fairly high-level ... group, we didn't have anything to offer," Graham said. "We hadn't had any time to think about it. We were still focused on Iraq."

Graham said that the Bush administration's approach slighted Moscow. "We missed some opportunities in the Bush administration's initial years to put this on a different track," Graham said. "And then later on, some of our actions, intentional or not, sent a clear message to Moscow that we didn't care."

THREE TRAIN WRECKS

Bush's relationship with Putin unraveled in 2008. In February, Kosovo unilaterally declared independence from Serbia with the support of the United States - a step that Russia, a longtime supporter of Serbia, had been trying to block diplomatically for more than a decade. In April, Bush won support at a NATO summit in Bucharest for the construction of a missile defense system in Eastern Europe.

Bush called on NATO to give Ukraine and Georgia a so-called Membership Action Plan, a formal process that would put each on a path toward eventually joining the alliance. France and Germany blocked him and warned that further NATO expansion would spur an aggressive Russian stance when Moscow regained power.

In the end, the alliance simply issued a statement saying the two countries "will become members of NATO." That compromise risked the worst of both worlds - antagonizing Moscow without giving Kiev and Tbilisi a roadmap to join NATO.

The senior U.S. official said these steps amounted to "three train wrecks" from Putin's point of view, exacerbating the Russian leader's sense of victimization. "Doing all three of those things in kind of close proximity - Kosovo independence, missile defense and the NATO expansion decisions - sort of fed his sense of people trying to take advantage of Russia," he said.

In August 2008, Putin struck back. After Georgia launched an offensive to regain control of the breakaway, pro-Russian region of South Ossetia, Putin launched a military operation that expanded Russian control of South Ossetia and a second breakaway area, Abkhazia.

The Bush administration, tied down in Iraq and Afghanistan, publicly protested but declined to intervene militarily in Georgia. Putin emerged as the clear winner and achieved his goal of standing up to the West.

ONLY ONE MAJOR ISSUE

After his 2008 election victory, Barack Obama carried out a sweeping review of Russia policy. Its primary architect was Michael McFaul, a Stanford University professor and vocal proponent of greater democracy in Russia who took the National Security Council position previously held by Thomas Graham.

In a recent interview, McFaul said that when Obama's new national security team surveyed the administration's primary foreign policy objectives, they found that few involved Russia. Only one directly related to bilateral relations with Moscow: a new nuclear arms reduction treaty.

The result, McFaul said, was that relations with Moscow were seen as important in terms of achieving other foreign policy goals, and not as important in terms of Russia itself.

"So that was our approach," he said.

Obama's new Russia strategy was called "the reset." In July 2009, he traveled to Moscow to start implementing it.

In an interview with the Associated Press a few days before leaving Washington, Obama chided Putin, who had become Russia's prime minister in 2008 after reaching his two-term constitutional limit as president. Obama said the United States was developing a "very good relationship" with the man Putin had anointed as his successor, Dmitry Medvedev, and accused Putin of using "Cold War approaches" to relations with Washington.

"I think Putin has one foot in the old ways of doing business and one foot in the new," Obama said.

In Moscow, Obama spent five hours meeting with Medvedev and only one hour meeting with Putin, who was still widely seen as the country's real power. After their meeting, Putin said U.S.-Russian relations had gone through various stages.

"There were periods when our relations flourished quite a bit and there were also periods of, shall we say, grayish mood between our two countries and of stagnation," he said, as Obama sat a few feet away.

At first, the reset fared well. During Obama's visit, Moscow agreed to greatly expand Washington's ability to ship military supplies to Afghanistan via Russia. In April 2010, the United States and Russia signed a new START treaty, further reducing the U.S. and Russian nuclear arsenals. Later that year, Russia supported sweeping new U.N. economic sanctions on Iran and blocked the sale of sophisticated, Russian-made S-300 anti-aircraft missile systems to Tehran.

Experts said the two-year honeymoon was the result of the Obama administration's engaging Russia on issues where the two countries shared interests, such as reducing nuclear arms, countering terrorism and nonproliferation. The same core issues that sparked tensions during the Bush administration - democracy and Russia's neighbors - largely went unaddressed.

A VAPORIZED RELATIONSHIP

In 2011, Putin accused Secretary of State Hillary Clinton of secretly organizing street demonstrations after disputed Russian parliamentary elections. Putin said Clinton had encouraged "mercenary" Kremlin foes. And he claimed that foreign governments had provided "hundreds of millions" of dollars to Russian opposition groups.

"She set the tone for some opposition activists, gave them a signal, they heard this signal and started active work," Putin said.

McFaul called that a gross exaggeration. He said the U.S. government and American non-profit groups in total have provided tens of millions of dollars in support to civil society groups in Russia and former Soviet bloc countries since 1989.

In 2012, Putin was elected to a third term as president and launched a sweeping crackdown on dissent and re-centralization of power. McFaul, then the U.S. ambassador in Moscow, publicly criticized the moves in speeches and Twitter posts.

In the interview, McFaul blamed Putin for the collapse in relations. McFaul said the Russian leader rebuffed repeated invitations to visit Washington when he was prime minister and declined to attend a G-8 meeting in Washington after he again became president. Echoing Bush-era officials, McFaul said it was politically impossible for an American president to trade Russian cooperation on Iran, for example, for U.S. silence on democracy in Russia and Moscow's pressuring of its neighbors.

"We're not going to do it if it means trading partnerships or interests with our partners or allies in the region," McFaul said. "And we're not going to do it if it means trading our speaking about democracy and human rights."

Andrew Weiss, a Russia expert at the Carnegie Endowment for International Peace, said that clashes over democracy ended any hopes of U.S.-Russian rapprochement, as they had in the Bush administration.

"That fight basically vaporizes the relationship," said Weiss.

In 2013, U.S.-Russian relations plummeted. In June, Putin granted asylum to National Security Agency whistleblower Edward Snowden. Obama, in turn, canceled a planned summit meeting with Putin in Moscow that fall. It was the first time a U.S. summit with the Kremlin had been canceled in 50 years.

Last fall, demonstrators in Kiev began demanding that Ukraine move closer to the European Union. At the time, the Obama White House was deeply skeptical of Putin and paying little attention to the former Soviet bloc, according to Weiss. White House officials had come to see Russia as a foreign policy dead end, not a source of potential successes.

Deferring to European officials, the Obama administration backed a plan that would have moved Ukraine closer to the EU and away from a pro-Russian economic bloc created by Putin. Critics said it was a mistake to make Ukraine choose sides.

Jack F. Matlock, who served as U.S. ambassador to Moscow from 1987 to 1991, said that years of escalating protests by Putin made it clear he believed the West was surrounding him with hostile neighbors. And for centuries, Russian leaders have viewed a friendly Ukraine as vital to Moscow's defense.

"The real red line has always been Ukraine," Matlock said. "When you begin to poke them in the most sensitive area, unnecessarily, about their security, you are going to get a reaction that makes them a lot less cooperative."

A PLIANT RUSSIA?

American experts said it was vital for the U.S. to establish a new long-term strategy toward Russia that does not blame the current crisis solely on Putin. Matthew Rojansky, a Russia expert at the Wilson Center, argued that demonizing Putin reflected the continued failure of American officials to recognize Russia's power, interest and importance.

"Putin is a reflection of Russia," Rojansky said. "This weird notion that Putin will go away and there will suddenly be a pliant Russia is false."

A senior U.S. official, who spoke on condition of anonymity, called for a long-term strategy that exploits the multiple advantages the U.S. and Europe enjoy over Putin's Russia.

"I would much rather be playing our hand than his over the longer term," the official said. "Because he has a number of, I think, pretty serious strategic disadvantages - a one-dimensional economy, a political system and a political elite that's pretty rotten through corruption."

Matlock, the former U.S. ambassador, said it was vital for Washington and Moscow to end a destructive pattern of careless American action followed by Russian overreaction.

"So many of the problems in our relationship really relate, I would say, to what I'd call inconsiderate American actions," Matlock said. "Many of them were not meant to be damaging to Russia. … But the Russian interpretation often exaggerated the degree of hostility and overreacted."

KIEV, Ukraine — For two weeks, the mysteriously well-armed, professional gunmen known as “green men” have seized Ukrainian government sites in town after town, igniting a brush fire of separatist unrest across eastern Ukraine. Strenuous denials from the Kremlin have closely followed each accusation by Ukrainian officials that the world was witnessing a stealthy invasion by Russian forces.

Now, photographs and descriptions from eastern Ukraine endorsed by the Obama administration on Sunday suggest that many of the green men are indeed Russian military and intelligence forces — equipped in the same fashion as Russian special operations troops involved in annexing the Crimea region in February. Some of the men photographed in Ukraine have been identified in other photos clearly taken among Russian troops in other settings.

And Ukraine’s state security service has identified one Russian reported to be active among the green men as Igor Ivanovich Strelkov, a Russian military intelligence operative in his mid- to late 50s. He is said to have a long résumé of undercover service with the Main Intelligence Directorate of the Russian general staff, most recently in Crimea in February and March and now in and around the eastern Ukrainian city of Slovyansk.

“There has been broad unity in the international community about the connection between Russia and some of the armed militants in eastern Ukraine, and the photos presented by the Ukrainians last week only further confirm this, which is why U.S. officials have continued to make that case,” Jen Psaki, the State Department spokeswoman, said Sunday.

The question of Russia’s role in eastern Ukraine has a critical bearing on the agreement reached Thursday in Geneva among Russian, Ukrainian, American and European diplomats to ease the crisis. American officials have said that Russia would be held responsible for ensuring that the Ukrainian government buildings were vacated, and that it could face new sanctions if the terms were not met.

The Kremlin insists that Russian forces are in no way involved, and that Mr. Strelkov does not even exist, at least not as a Russian operative sent to Ukraine with orders to stir up trouble. “It’s all nonsense,” President Vladimir V. Putin said Thursday during a four-hour question-and-answer session on Russian television. “There are no Russian units, special services or instructors in the east of Ukraine.” Pro-Russian activists who have seized government buildings in at least 10 towns across eastern Ukraine also deny getting help from professional Russian soldiers or intelligence agents.

But masking the identity of its forces, and clouding the possibilities for international denunciation, is a central part of the Russian strategy, developed over years of conflict in the former Soviet sphere, Ukrainian and American officials say.

John R. Schindler, a former National Security Agency counterintelligence officer who now teaches at the Naval War College, calls it “special war”: “an amalgam of espionage, subversion, even forms of terrorism to attain political ends without actually going to war in any conventional sense.”

And one country, Mr. Schindler noted in an article last year in which he coined the term, that particularly excels at special war is Russia, which carried out its first post-Soviet war to regain control of rebellious Chechnya back in 1994 by sending in a column of armored vehicles filled with Russian soldiers masquerading as pro-Moscow Chechens.

Russia’s flair for “maskirovka” — disguised warfare — has become even more evident under Mr. Putin, a former K.G.B. officer whose closest advisers are mostly from that same Soviet intelligence agency.

For nearly two months now, the shaky new Ukrainian government has been left to battle phantoms, first in Crimea and now in eastern Ukraine, where previously fringe pro-Russian political activists have had their fortunes lifted by small but heavily armed groups of masked men.

In the eastern city of Slovyansk, under the control of pro-Russian insurgents for more than a week now, the green men have worked hard to blend in with locals but have occasionally let the mask slip, apparently to send a clear message that any push to regain control by Ukrainian forces would risk bringing down the wrath of the Russian military.

A gradation of forces control the city and other areas now in the hands of separatist rebels, ranging from clearly professional masked soldiers and unruly groups of local men in camouflage, rifles slung over their shoulders, to teenage boys in sweatpants carrying baseball bats or hunting knives. At most times, only the local toughs are visible on the streets.

But when a woman sidled up to one of the masked gunmen in the city’s central square last week and asked where he was from, she got an answer that summed up Russia’s bedeviling and constantly shifting disguises. The gunman initially said he was “from Russia,” but when pressed, said coyly that he was “from New Russia,” a long-forgotten czarist-era term revived last week by Mr. Putin to describe a large section of eastern and southern Ukraine.

Asked by the woman what would happen if the Ukrainian Army attacked, he replied, “We have to stand for only 24 hours, to tend the fire, and after that, a one million man army will be here.”

When a Ukrainian armored column approached the town last Wednesday and then swiftly surrendered, a group of disciplined green men suddenly appeared on the scene and stood guard. Over the course of several hours, several of them told bystanders in the sympathetic crowd that they were Russians. They allowed themselves to be photographed with local girls, and drove an armored personnel carrier in circles to please the crowd.

“It’s hard to fathom that groups of armed men in masks suddenly sprang forward from the population in eastern Ukraine and systematically began to occupy government facilities,” Gen. Philip M. Breedlove, NATO’s top military commander, wrote in a blog post on the alliance’s website. “It’s hard to fathom because it’s simply not true. What is happening in eastern Ukraine is a military operation that is well planned and organized, and we assess that it is being carried out at the direction of Russia.”

His evidence, however, was mostly circumstantial: Pro-Russian gunmen “exhibit telltale military training and equipment”; they handle weapons like professional soldiers, not new recruits to a pickup “self-defense” force; they carry weapons and equipment that are primarily Russian Army issue, not gear “that civilians would be likely to be able to get their hands on in large numbers.” General Breedlove conceded that such points, taken alone, might not prove much, “but taken in the aggregate, the story is clear.”

Heightening skepticism of Russia’s denials is also the fact that Mr. Putin, after denying any Russian link to the masked gunmen who seized government buildings in Crimea and blockaded Ukrainian military bases there, last week changed his story and said, “Of course, Russian servicemen did back the Crimean self-defense forces.”

More direct evidence of a Russian hand in eastern Ukraine is contained in a dossier of photographs provided by Ukraine to the Organization for Security and Cooperation in Europe, a Vienna-based organization now monitoring the situation in Donetsk and other parts of the country. It features pictures taken in eastern Ukraine of unidentified gunmen and an earlier photograph of what looks like the same men appearing in a group shot of a Russian military unit in Russia.

One set of photographs shows what appears to be the same gunman in pictures taken in the Crimean annexation and more recently in Slovyansk. Another features a portly bearded man photographed in Slovyansk on April 14, wearing a camouflage uniform without insignia, but six years earlier, had been photographed during Russia’s invasion of Georgia with a Russian special forces patch on his left arm.

Another character in Ukraine’s case against Russia is Mr. Strelkov, the alleged military intelligence officer who Kiev says took part in a furtive Russian operation to prepare for the annexation of Crimea and, more recently, in insurgent action in Slovyansk.

No photographs have yet emerged of Mr. Strelkov, but the Security Service of Ukraine, the successor organization to what used to be Ukraine’s local branch of the K.G.B., has released a sketch of what it says is his face.

The security agency, known by its Ukrainian abbreviation S.B.U., first identified him publicly early last week after releasing an audio recording of what it said was a recording of an intercepted communication between Russian operatives in eastern Ukraine and their controller back in Russia.

In the recording, a man nicknamed “Strelok” — who the Ukrainian agency says is Mr. Strelkov — and others can be heard discussing weapons, roadblocks and how to hold on to captured positions in and near Slovyansk with a superior in Russia.

The superior, clearly anxious to keep Russia’s role hidden, can be heard ordering his men on the ground in Ukraine not to identify themselves and to find someone with a Ukrainian accent who can give an interview to a Russian television channel. It was very important, he added, to say on air that all the pro-Russian insurgents want is “federalization,” or constitutional changes to give eastern Ukraine more autonomy.

Military analysts say the Russian tactics show a disturbing amount of finesse that speak to long-term planning.

“The Russians have used very specialized, very effective forces,” said Jacob W. Kipp, an expert on the Russian military and the former deputy director of the United States Army’s School of Advanced Military Studies at Fort Leavenworth, Kan.

“They don’t assume that civilians are cluttering up the battlefield; they assume they are going to be there,” he said. “They are trained to operate in these kind of environments.”