"There is no doubt that this is inappropriate," said Arlen Specter, a Republican, calling hearings early next year "a very, very high priority".
Fellow Republican Senator John McCain, who challenged George Bush, the US president, for the White House in 2000 said the story about the National Security Agency's actions, first reported in Friday's New York Times, was troubling.
The NSA is normally barred from eavesdropping within the country, and the report is expected to trigger debate about whether the practice violates the US constitution.
US authorities normally need court orders before they can conduct spying within the country.
Neither Condoleezza Rice, the US secretary of state, nor White House press secretary Scott McClellan would confirm or deny the report which said the super-secret NSA had spied on as many as 500 people at any given time since 2002 in this country.
"This is Big Brother run amok"
That year, following the September 11 attacks, Bush authorised the NSA to monitor the international phone calls and international e-mails of hundreds - perhaps thousands - of people inside the United States, the Times reported.
McClellan said the White House has received no requests for information from lawmakers because of the report.
"Congress does have an important oversight role," he said.
Before the programme began, the NSA typically limited its domestic surveillance to foreign embassies and missions and obtained court orders for such investigations.
Overseas, 5000 to 7000 people suspected of terrorist ties are monitored at one time.
"This is Big Brother run amok," declared Democratic Senator Edward Kennedy.
Senator Russell Feingold called it a "shocking revelation" that "ought to send a chill down the spine of every senator and every American".
Administration officials reacted to the report by asserting that the president has respected the constitution while striving to protect the American people.
"[The president is] fully committed to upholding our constitution and protect the civil liberties of the American people. And he has done both"
White House press secretary
Rice said Bush had "acted lawfully in every step that he has taken". And McClellan said Bush "is going to remain fully committed to upholding our constitution and protect the civil liberties of the American people. And he has done both".
The report surfaced as the administration and its Republican allies on Capitol Hill were fighting to save provisions of the expiring USA Patriot Act that they believe are key tools in the fight against terrorism.
An attempt to rescue the approach favoured by the White House and Republicans failed on Friday morning.
The Times said reporters interviewed nearly a dozen current and former administration officials about the programme and granted them anonymity because of the classified nature of the programme.
Government officials credited the new programme with uncovering several terrorist plots, including one by Iyman Faris, an Ohio trucker who pleaded guilty in 2003 to supporting al-Qaida by planning to destroy the Brooklyn Bridge, the report said.
Some NSA officials were so concerned about the legality of the programme that they refused to participate, the Times said.
Questions about the legality of the programme led the administration to temporarily suspend it last year and impose new restrictions.
Asked about this on NBC's "Today" show, Rice said, "I'm not going to comment on intelligence matters".
"I can only comment to say that the president has been very clear that he has not ordered people to do things that are illegal," she added.
Caroline Fredrickson, director of the Washington legislative office of the American Civil Liberties Union, said the group's initial reaction to the NSA disclosure was "shock that the administration has gone so far in violating American civil liberties to the extent where it seems to be a violation of federal law".