France's CNIL agency said on Monday that European data protection agencies "consider they should evaluate the exact impact of the PRISM programme on the privacy and data of European citizens," and have written to the European Commission for its help to get information from the United States.
Revelations about PRISM and other programmes by the US National Security Agency (NSA) to capture and store personal information gleaned from emails, phone calls and web searches have sparked outrage in Europe, especially after tech giants such as Google and Facebook were implicated.
The revelations threatened the start last month of crucial EU-US free trade talks, but Europe agreed to go ahead with the negotiations after a joint working group was formed to investigate the spying.
In a letter to European Commission Vice President Viviane Reding, the agencies said the "collection of and access by the American intelligence community to data on non-US persons are of great concern to the international data protection community."
Despite some clarifications from Washington, "many questions as to the consequences of these intelligence programmes remain," it said.
It said the agencies had a duty to "assess independently to what extent the protection provided by EU data protection legislation is at risk and possibly breached" by the US intelligence-gathering programme.
Reding, who is also the EU's justice commissioner, said last month the EU was determined to deliver new European data protection laws in the wake of the revelations.
European sources have said governments' anger over the data surveillance is genuine, following reports of widespread spying on Washington's European allies.
Snowden, a 30-year-old former NSA contractor, received asylum in Russia on August 1st, after spending more than five weeks stranded in a Moscow airport avoiding extradition to the United States.
He is wanted by Washington on espionage charges linked to his media disclosures about the secret details of the US surveillance programmes.
US President Barack Obama has defended the spy programmes as a "modest encroachment" on privacy necessary to keep Americans safe.
French officials, however, including President François Hollande, have responded angrily to revelations that the NSA had spied on its embassy in Washington D.C.
In July, two French rights organisations vowed to file suit in France, in order to discover whether US-based giants like Facebook, Google and Yahoo had played a role in the electronic surveillance.
At the time, the International Federation of Human Rights (FIDH) and the French League of Human Rights (LDH) attacked the mass surveillance of global communications by US intelligence services that was carried out "under the guise of the fight against terrorism and organised crime".
"This uncontrolled intrusion into people's lives is a significant threat to individual liberties and must be curbed at the risk of seeing the rule of law disappear," the groups said in a joint statement.