WASHINGTON – Responding to congressional pressure from both parties, the White House agreed yesterday to give lawmakers more information about its wiretapping program, although the briefings remain highly classified and limited in scope.

Despite the administration’s overture, several prominent Republicans said they will pursue legislation enabling Congress to conduct more aggressive oversight of the National Security Agency’s warrantless monitoring of Americans’ phone calls and emails. Recent disclosure of the four-year-old program has alarmed civil libertarians and divided the GOP, with many Republicans defending the operation and others calling for more information and regulation.

Yesterday Attorney General Alberto Gonzales and former NSA director Michael Hayden briefed the House intelligence committee, behind closed doors, for nearly four hours. The panel “was given some additional procedural information to provide a fuller understanding of how carefully tailored and monitored this program is,” White House spokeswoman Dana Perino said. She said she did not think the information included estimates of the number of Americans who have been secretly monitored. Numerous lawmakers have said such information is important to help Congress gauge the program’s legality and effectiveness.

Messrs. Gonzales and Hayden were scheduled to brief the committee only on legal rationales for the program, not procedural or operations aspects, House sources said. Shortly before the afternoon hearing began, the two men agreed to broaden the discussion, the sources said.

The committee’s ranking Democrat, Jane Harman of California who has pressed the administration to be more forthcoming so Congress can assess the program and provide needed oversight – told reporters that “the ice is falling.”

Committee Chairman Peter Hoekstra, a Republican of Michigan, said in a statement: “Today’s briefing was a positive first step, and I appreciate the White House’s willingness to inform more members on aspects of this vital NSA program. While the briefing did not, and could not, cover the full operational aspects of the program, it will allow for increased committee oversight going forward.”

The briefing occurred one day after Rep. Heather Wilson, a Republican of New Mexico, who chairs the House intelligence subcommittee that oversees the NSA, told the New York Times she wanted a full congressional inquiry into the surveillance program. Yesterday Ms. Wilson stepped away from the hearing to tell reporters,”This is a very positive development.

Serious questioning,sharing of information and review of this program began this afternoon … The checks and balances in our system of government are very important, and it’s those checks and balances that are going on and being executed now.”

Ms. Wilson faces a stiff re-election challenge this fall from New Mexico’s Democratic Attorney General Patricia Madrid.

Despite yesterday’s White House comments, Senate Judiciary Committee Chairman Arlen Specter, a Republican of Pennsylvania, announced that he is drafting a bill that would “require the administration to take the program to the Foreign Intelligence Surveillance Court.” The secretive court was established in 1978 to handle Justice Department requests for warrants to monitor communications of terrorism and espionage suspects.

The administration recently acknowledged that in 2001 it began eavesdropping on an undisclosed number of communications without alerting the FISA court or seeking warrants. Each targeted communication involves a person in America and one outside, Mr. Gonzales told the Senate panel this week, and at least one of the persons is suspected of a possible tie to terrorists.The Washington Post reported Sunday that thousands of Americans appear to have been monitored, resulting in very few communications that the NSA deemed worthy of further pursuit. Messrs. Gonzales and Hayden have declined to confirm or dispute the article’s chief findings.

Several GOP lawmakers have defended the NSA program, saying the administration has given Congress all the information it needs and deserves. But some prominent Republicans have joined Mr. Specter and Ms. Wilson in questioning whether the program complies with the FISA law, and in calling for more information without divulging important secrets.

Senator Hagel, a Republican of Nebraska, said in an interview, the “balance must be preserved between the executive branch and the legislature.And I think this is a clear example of where the balance has gotten skewed. … The administration cannot unilaterally assume that they have the answers to get around or go over a law.” Mr. Hagel sits on the Senate intelligence committee, which will be privately briefed today by Messrs. Gonzales and Hayden.