Two human rights groups have filed a lawsuit in Paris seeking an investigation into whether the US National Security Agency violated French privacy laws by secretly collecting massive amounts of personal data.

The legal complaint against persons unknown aims to prompt a judicial investigation that would also look at the alleged role of tech companies including Facebook, Apple, Google, Yahoo, Microsoft and Skype in data-gathering by the NSA.

The France-based International Federation for Human Rights (FIDH) and the Human Rights League based the complaint on disclosures by the NSA leaker Edward Snowden which indicated that the US government amassed phone and internet usage data on people around the world for security reasons.

Lawyers for the two groups said that such surveillance, if confirmed, would violate up to five French privacy laws, including illicit collection of personal data and the infringement of the right to a private life.

Patrick Baudouin, of the FIDH, estimated that thousands of French people may be regularly targeted by the surveillance. He said that although the lawsuit was limited to French jurisdiction, he hoped it could lead to wider pressure on the US.

Emmanuel Daoud, a lawyer for the FIDH, told France Info radio that the NSA disclosures revealed an "incredible scandal". He said he had never seen "such a massive attack on individual liberties by a foreign state, because it potentially concerns every French citizen and internet user" and the "unauthorised collection of a massive amount of personal information".

He said one clear aim of the lawsuit was to demand explanations from internet giants about whether, as Snowden's documents claimed, direct access was given to servers as part of surveillance.

The companies involved vigorously deny giving the US administration backdoor access to users' information. If a judicial investigation is opened in France, the French subsidiaries of such firms could be questioned.

Le Monde reported last week that France's external intelligence agency, the DGSE, runs its own vast electronic surveillance operation, intercepting and stocking data from citizens' phone and internet activity using similar methods to the NSA's Prism programme exposed by Snowden. The paper said rights groups were considering possible legal action over illegal French surveillance tactics.

This week lawyers acting for the UK charity Privacy International filed a legal challenge against British and US spy programmes that allow intelligence agencies to gather, store and share data on millions of people.

They also demanded a temporary injunction to the Tempora programme, which allows Britain's spy centre GCHQ to harvest millions of emails, phone calls and Skype conversations from the undersea cables that carry internet traffic in and out of the country. They said the laws being used to justify mass data-trawling were being abused by intelligence officials and ministers, and needed to be urgently reviewed.