The first constitutional challenge to the widespread surveillance of US citizens disclosed by the whistleblower Edward Snowden was laid down on Tuesday, as international pressure on the Obama administration over the scale of the dragnet intensified.

In a lawsuit filed in New York, the American Civil Liberties Union accused the US government of a process that was "akin to snatching every American's address book".

On Capitol Hill, a group of US senators introduced a bill aimed at forcing the US federal government to disclose the opinions of a secretive surveillance court that determines the scope of the eavesdropping on Americans' phone records and internet communications.

Separately, a leading member of the Senate intelligence committee came close to saying that James Clapper, the US director of national intelligence, misled him on the scope of government surveillance during a March hearing.

In Brussels, the European commission's vice-president, Viviane Reding, sent a letter demanding answers to seven detailed questions to the US attorney general, Eric Holder, demanding explanations about Prism and other American data snooping programmes.

As the fallout from the revelations by Edward Snowden continued, the defense secretary, Chuck Hagel, said he ordered a wide-ranging review of the Defense Department's reliance on private contractors. Snowden, 29, had top-security clearance for his work at Booz Allen Hamilton, an NSA contractor. Booz Allen issued a statement on Tuesday saying that Snowden had been fired for "violations of the firm's code of ethics".

Photos of Edward Snowden, the NSA whistleblower, and President Barack Obama appear on the front pages of local English and Chinese newspapers in Hong Kong on 11 June 2013. Photograph: Bobby Yip/Reuters

Snowden checked out of the hotel where he was staying in Hong Kong on Monday and moved to an undisclosed location. The director of Human Rights Watch, Peter Bouckaert, said Snowden should not consider himself protected in the Chinese province. "I certainly would not consider Hong Kong a safe place for him at the moment," said Bouckaert, who after the fall of Muammar Gaddafi found faxes in Tripoli indicating that the Hong Kong authorities had co-operated with the CIA in rendering an anti-Gaddafi Islamist to Libya.

A spokesman for Vladimir Putin said that if Snowden applied for asylum in Russia, the request would be considered.

Snowden left Hawaii for Hong Kong three weeks ago, telling his girlfriend, Lindsay Mills, that he was going away for a while but was deliberately vague about the reason for his disappearance. A blogpost, apparently written by Mills, a 28-year-old performance artist, said: "My world has opened and closed all at once. Leaving me lost at sea without a compass … at the moment all I can feel is alone."

Lindsay Mills, the acrobat girlfriend of NSA whistleblower Edward Snowden, strikes poses for a photoshoot in Hawaii. Photograph: Splash/Luis SilosIII Photography/Splash

The authenticity of the blog, which was seen by the Guardian before it was taken down on Tuesday, could not be verified. However, Snowden had previously told the Guardian his girlfriend was called Lindsay.

The constitutional implications of Snowden's revelations were addressed in the ACLU's law suit, filed in the Southern District of New York. It claimed the National Security Agency's acquisition of phone records of millions of Verizon users, obtained in April through an order by the secret Fisa court and revealed by the Guardian, violates the first and fourth amendments, which guarantee citizens' right to association, speech and to be free of unreasonable searches and seizures. As a Verizon subscriber, the ACLU claimed standing to sue.

The suit also claims that the surveillance goes beyond the authorisation provided by section 215 of the Patriot Act, a claim made for years by two leading Democratic members of the Senate intelligence committee, Ron Wyden of Oregon and Mark Udall of Colorado.

Wyden revealed on Tuesday that he had given Clapper, the director of national intelligence, a day's advance notice of a question about the extent of government surveillance at a congressional hearing earlier this year.

When asked directly by Wyden in March whether the NSA was collecting any kind of data on "millions" of Americans, Clapper replied "no" and "not wittingly" – a claim undermined by the Guardian's disclosures about NSA collection of millions of Americans' phone records. Wyden disclosed that he had given Clapper an opportunity in private to revise his answer, after the session. Clapper said earlier this week that he had answered the question in the "least untruthful" way possible.

James Clapper, who issued a stinging attack on the intelligence leaks this weekend, is a former Booz Allen executive Photograph: Susan Walsh/AP

In statement on Tuesday, Wyden said: "One of the most important responsibilities a senator has is oversight of the intelligence community. This job cannot be done responsibly if senators aren't getting straight answers to direct questions."

The office of Senator Jeff Merkley said he planned to introduce a bill on Tuesday that would compel the first public airing of the so-called Fisa court's understandings of section 215 of the Patriot Act, which the government has cited as the basis for collecting the phone records of millions of Americans; and section 702 of the 2008 Fisa Amendments Act, which the government has cited as the basis for NSA internet monitoring program known as Prism.

"I think that Americans deserve to know how our government is interpreting the Patriot Act and the Fisa Amendments Act," Jamal Raad, a spokesman for Merkley, told the Guardian on Tuesday.

The Obama administration has said all its surveillance efforts are subject to rigorous Fisa court review and members of congress are sufficiently briefed on them, even though most legislators did not receive such briefings.

US authorities faced challenges on other fronts: Google's chief legal counsel wrote to the Justice Department to request its ability to detail its co-operation with the government on surveillance orders, largely in the hope of assuring customers that it does not turn over user data wholesale to the NSA.

"Google's numbers would clearly show that our compliance with these requests falls far short of the claims being made," wrote Google's David Drummond. "Google has nothing to hide."

Similarly, a new coalition of privacy groups, internet companies and activists, called Stop Watching Us, unveiled itself Tuesday to demand "the US Congress reveal the full extent of the NSA's spying programs," which amount to "a stunning abuse of our basic rights." The coalition includes Mozilla, Reddit, John Cusack and the ACLU, among others.

The NSA affair continued to have international ramifications. In the European commission letter, Reding warns Holder that "given the gravity of the situation and the serious concerns expressed in public opinion on this side of the Atlantic" she expects detailed answers before they meet at an EU-US justice ministers' meeting in Dublin on Friday.

In the letter, which has been released to the Guardian, Reding details her serious concerns that the Americans are "accessing and processing, on a large scale, the data of EU citizens using major US online service providers". She says that programmes such as Prism, and the laws that authorise them, could have "grave adverse consequences for the fundamental rights of EU citizens".

She also warns Holder that the nature of the American response could affect the whole transatlantic relationship.