Barack Obama was facing a mounting domestic and international backlash against US surveillance operations on Monday as his administration struggled to contain one of the most explosive national security leaks in US history.

Political opinion in the US was split with some members of Congress calling for the immediate extradition from Hong Kong of the whistleblower, Edward Snowden. But other senior politicians in both main parties questioned whether US surveillance practices had gone too far.

Dianne Feinstein, chairman of the national intelligence committee, has ordered the NSA to review how it limits the exposure of Americans to government surveillance. But she made clear her disapproval of Snowden. "What he did was an act of treason," she said.

Officials in European capitals demanded immediate answers from their US counterparts and denounced the practice of secretly gathering digital information on Europeans as unacceptable, illegal and a serious violation of basic rights. The NSA, meanwhile, asked the Justice Department to open a criminal investigation and said that it was assessing the damage caused by the disclosures.

Daniel Ellsberg, the former military analyst who revealed secrets of the Vietnam war through the Pentagon Papers in 1971, described Snowden's leak as even more important and perhaps the most significant leak in American history.

Snowden disclosed his identity in an explosive interview with the Guardian, published on Sunday, which revealed he was a 29-year-old former technical assistant for the CIA and current employee of the defence contractor Booz Allen Hamilton. Snowden worked at the National Security Agency for the past four years as an employee of various outside contractors, including Booz Allen and Dell.

In his interview, Snowden revealed himself as the source for a series of articles in the Guardian last week, which included disclosures of a wide-ranging secret court order that demanded Verizon pass to the NSA the details of phone calls related to millions of customers, and a huge NSA intelligence system called Prism, which collects data on intelligence targets from the systems of some of the biggest tech companies.

Snowden said he had become disillusioned with the overarching nature of government surveillance in the US. "The government has granted itself power it is not entitled to. There is no public oversight. The result is people like myself have the latitude to go further than they are allowed to," he said.

"My sole motive is to inform the public as to that which is done in their name and that which is done against them."

As media interest intensified on Monday, Snowden checked out of the Hong Kong hotel where he had been staying, and moved to an undisclosed location.

Reacting to Snowden's revelations, Paul Ryan, the former Republican vice-presidential nominee, raised questions about whether privacy was being unduly threatened. "I'm sure somebody can come up with a great computer program that says: 'We can do X, Y, and Z,' but that doesn't mean that it's right," he told a radio station in Wisconsin. "I want to learn a lot more about it on behalf of the people I represent," he added.

Pressure was growing on the White House to explain whether there was effective congressional oversight of the programmes revealed by Snowden. The director of national intelligence, James Clapper, said in an NBC interview that he had responded in the "least untruthful manner" possible when he denied in congressional hearings last year that the NSA collected data on millions of Americans.

Clapper also confirmed that Feinstein had asked for a review to "refine these NSA processes and limit the exposure to Americans' private communications" and report back "in about a month".

In Europe, the German chancellor Angela Merkel indicated she would press Obama on the revelations at a Berlin summit next week, while deputy European Commission chief Viviane Reding said she would press US officials in Dublin on Friday, adding that "a clear legal framework for the protection of personal data is not a luxury or constraint but a fundamental right".

Peter Schaar, Germany's federal data protection commissioner told the Guardian that it was unacceptable that US authorities have access to the data of European citizens "and the level of protection is lower than what is guaranteed for US citizens." His Italian counterpart, Antonello Soro, said that the data dragnet "would not be legal in Italy" and would be "contrary to the principles of our legislation and would represent a very serious violation".

In London, the British foreign secretary William Hague was forced to defend the UK's use of intelligence gathered by the US. In the House of Commons, Hague told MPs that British laws did not allow for "indiscriminate trawling" for information. "There is no danger of a deep state out of control in some way," he said.

But Hague was reluctant to go into detail on how Britain handled information offered by US intelligence agencies, as opposed to information requested, or whether it was subject to the same ministerial oversight, including warrants.

Civil liberties groups ask for review of 'secret law'

The Obama administration offered no indication on Monday about what it intended to do about Snowden. The White House did however say he had sparked an "appropriate debate" and hinted it might welcome revision of the Patriot Act, legislation introduced in 2001 which it claims gives legal authority for the programmes carried out by the National Security Agency.

"If [congressional] debate were to build to a consensus around changes [to the Patriot Act] the president would look at that," said spokesman Jay Carney. "Although this is hardly the manner of discussion we hoped for, we would still like to have the debate."

The first polls since the leak stories first broke indicated that the majority of Americans oppose the government scooping up their phone data. According to the Rasmussen poll just 26% of voters are in favour of the government's collection of data from Verizon while 59% are opposed. In total 46% of Americans think that their own data has been monitored. But a poll by the Pew Research Center, asking a more general question, said 56% respondents approved of the NSA surveillance program.

The ACLU and Yale Law School's Media Freedom and Information Clinic filed a motion on Monday asking for secret Foreign Intelligence Surveillance Court opinions on the Patriot Act to be made public in the light of the Guardian's revelations.

The motion asks for any documents relating to the court's interpretation of the scope, meaning and constitutionality of Section 215 of the Patriot Act – which authorises government to obtain "any tangible thing" relevant to foreign intelligence or terrorism investigations – to be published "as quickly as possible" and with only minimal redaction.

"In a democracy, there should be no room for secret law," said Jameel Jaffer, ACLU deputy legal director. "The public has a right to know what limits apply to the government's surveillance authority, and what safeguards are in place to protect individual privacy."

There was support for Snowden among civil liberty activists. Ellsberg wrote for the Guardian: "In my estimation, there has not been in American history a more important leak than Edward Snowden's release of NSA material – and that definitely includes the Pentagon Papers 40 years ago".

The Electronic Frontier Foundation, an internet rights group, called for a "new Church committee" to investigate potential government infringements on privacy and to write new rules protecting the public. In the wake of the Watergate affair in the mid-1970s, a Senate investigation led by Idaho senator Frank Church uncovered decades of serious abuse by the US government of its eavesdropping powers. The committee report led to the passage of the Foreign Intelligence Surveillance Act and set up the Fisa courts that today secretly approve surveillance requests.

Both Snowden and the Obama administration appeared to be considering their options on Monday. Hong Kong, which has an extradition treaty with the US, is unlikely to offer Snowden a permanent refuge. But Snowden could buy time by filing an asylum request, thanks to a landmark legal ruling that has thrown the system into disarray.

The Foreign Correspondents' Club of Hong Kong said the case could be a "strong test" of the Chinese province's commitment to freedom of expression. "The FCC will watch closely how the SAR [Hong Kong] government handles his case, and in particular how it responds to any pressure from authorities both in Washington and Beijing to restrict his activities or to impede access by the media," it said in a statement.

In New York, the mayor, Michael Bloomberg, cancelled at very short notice a planned photo opportunity with the Hong Kong chief executive, Leung Chun-ying. "It would have been a circus, so we decided to catch up with him another time," a mayoral spokesman told the Guardian.

Additional reporting by Matt Williams and Tom McCarthy in New York.