The Obama administration was facing renewed pressure over the secrecy of its surveillance programs, as a group of US senators demanded it reveal how it interprets the laws that underpin them and foreign governments expressed growing concern.

A bill, to be introduced in the Senate on Tuesday, would force the US 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, members of the European parliament threatened to unpick data-sharing agreements with the US.

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".

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 the Russian president, 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. In a blogpost on Monday, apparently written by Mills, a 28-year-old performance artist, she wrote: "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." The website was later taken down.

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.

In Washington, 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.

Ron Wyden, a Democratic member of the Senate intelligence committee, revealed 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 in March.

Clapper said earlier this week that he had misunderstood the question. 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 also disclosed that he had given Clapper an opportunity in private to revise his answer, after the session.

"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," Wyden said in a statement on Tuesday.

The fallout from the affair continued to have international ramifications. German government spokesman Steffen Seibert told reporters on Monday that the chancellor, Angela Merkel, would question Obama about the NSA program when he visits Berlin on 18 June. The issue could tarnish a visit that both sides had hoped would reaffirm strong German-American ties.

In a heated debate in the European parliament on Tuesday, lawmakers complained that for a decade they had yielded to US demands for access to European financial and travel data and said it was time to re-examine the deals and to limit data access.

"We need to step back here and say clearly: mass surveillance is not what we want," said Jan Philipp Albrecht, a German Green lawmaker in charge of overhauling the EU's outdated data protection laws.

Lawmakers said the EU privacy overhaul and existing transatlantic data-sharing deals – the Swift agreement on sharing financial transaction data and an agreement on airline passenger name records – were in jeopardy. "It is time we grasped the nettle here and put our minds to ending the program," said Martin Ehrenhauser, an Austrian independent member of the European parliament.

Additional reporting by Paul Owen in London and the Associated Press