PARIS (AP) — Two human rights groups filed a lawsuit in Paris on Thursday seeking an investigation into whether the U.S. National Security Agency violated French privacy laws by secretly collecting huge amounts of personal data.

Privacy rights groups are trying to put pressure on the U.S. after disclosures by NSA leaker Edward Snowden indicating that the U.S. government amasses phone and Internet usage data on people around the world for security reasons. The lawsuit filed Thursday was based on those leaks, and comes after a London-based advocacy group filed a similar suit Monday.

The France-based International Federation for Human Rights and Human Rights League say that such surveillance, if confirmed, would violate up to five French privacy laws. Their lawyer Patrick Baudouin estimated that thousands of French people may be regularly targeted by the surveillance.

Baudouin says that while the lawsuit is limited to French jurisdiction, he hopes that it can lead to wider pressure on the U.S.

The lawsuit, like many in France, does not name the NSA or any particular target, but seeks to establish responsibility for eventual privacy violations.

"The lawsuit is subject to French legislation, and applies to French citizens. But this goes beyond France," he said. "If French authorities can determine responsibility, that could also profit other European citizens."

He noted that he himself could have been a target of surveillance, since he has defended terrorist suspects in the past.

In the U.S., groups including the Electronic Privacy Information Center and the American Civil Liberties Union have said they are suing over the NSA spying.

In Britain, the London suit by Privacy International could have ramifications for U.S.-U.K. intelligence sharing. Privacy International alleges that the NSA and its British counterpart GCHQ are spying on one another's citizens and swapping the intercepted information without proper oversight. The complaint also accuses GCHQ of overstepping British law through the mass monitoring of U.K. communications. However, legal experts say Privacy's complaint faces long odds at Britain's Investigatory Powers Tribunal.