Allegations that President George Bush authorised security agents to eavesdrop on people inside the US have caused a storm of protest.
Bush's top aides say he did not break the law
The New York Times says the National Security Agency was allowed to spy on hundreds of people without warrants.
The NSA is normally barred from eavesdropping within the US.
Republican Senator John McCain called for an explanation, while Senator Arlen Specter, Senate Judiciary Committee chairman, said he would investigate.
"There is no doubt that this is inappropriate," said Mr Specter, also a Republican, adding that Senate hearings would be held early next year as "a very, very high priority".
The allegations coincided with a setback for the Bush administration, as the Senate rejected extensions to spying provisions in the Patriot Act.
The New York Times said Mr Bush signed a secret presidential order following the attacks on 11 September 2001, allowing the NSA, based at Fort Meade, Maryland, to track the international telephone calls and e-mails of hundreds of people without referral to the courts.
Previously, surveillance on American soil was generally limited to foreign embassies.
Critics have questioned whether wider surveillance in the US crosses constitutional limits on legal searches.
American law usually requires a secret court, known as a Foreign Intelligence Surveillance Court, to give permission before intelligence officers can conduct surveillance on US soil.
Administration officials refused to confirm or deny details of the New York Times report, but issued a robust defence of anti-terrorist operations, saying they had prevented several attacks - including one on targets in Britain.
In an interview with US TV, Mr Bush said the administration did not discuss ongoing intelligence operations to protect the country.
NATIONAL SECURITY AGENCY
Formed in 1952
Biggest US security agency, with 38,000 employees
Nicknamed "No Such Agency"
Has a dozen listening posts around the world, tracking phone calls, diplomatic traffic, emails, faxes
May record up to 500 million hours of traffic every day
On US soil, can only listen to "agents of a foreign power"
But he added: "I will make this point. That whatever I do to protect the American people, and I have an obligation to do so, that we will uphold the law, and decisions made are made understanding we have an obligation to protect the civil liberties of the American people.
"I think the point that Americans really want to know is twofold. One, are we doing everything we can to protect the people? And two, are we protecting civil liberties as we do so? And my answer to both is: yes, we are."
The New York Times said nearly a dozen current and former administration officials had discussed the bugging programme, but that the paper delayed publishing its revelations for a year in response to White House concerns it could jeopardise investigations.
A former senior official who specialises in national security law told the paper that Mr Bush's move represented a "sea change".
"It's almost a mainstay of this country that the NSA only does foreign searches," said the anonymous source.
"This is Big Brother run amok," was the reaction of Democratic Senator Edward Kennedy, while his colleague Russell Feingold called it a "shocking revelation" that "ought to send a chill down the spine of every senator and every American".
The American Civil Liberties Union (ACLU) said eavesdropping in the US without a court order and without complying with the procedures of the Foreign Intelligence Surveillance Act was "both illegal and unconstitutional".
"The administration is claiming extraordinary presidential powers at the expense of civil liberties and is putting the president above the law," director Caroline Fredrickson said.
Senators from both sides have expressed disquiet
To opponents of the Bush administration, the alleged bugging programme is reminiscent of the widespread abuse of power by the security services during the Vietnam War when anti-war activists were monitored illegally, says BBC Washington correspondent Justin Webb.
That activity prompted tougher regulation of bugging.
In a separate development on Friday, the Senate refused to reauthorise provisions of the Patriot Act, extending government surveillance rights.
It is a sign of intense concern about infringements of civil liberties in the name of security, our correspondent says.
The White House is having a tough time convincing even its Republican supporters that the things it does in the name of the war on terrorism are always justified, he adds.