Senator Specter said details he will get today on a government surveillance program will help determine whether he’ll back the appointment of a special prosecutor to investigate Attorney General Gonzales’s congressional testimony.

Mr. Gonzales came under a new round of criticism last week over what some lawmakers said were contradictions in statements about the debate within the Bush administration regarding a terrorist surveillance program. Senate Democrats have asked for appointment of a special counsel to look into whether the attorney general lied under oath.

“We do not know if the administration has been leveling with us or not on the terrorist surveillance program,” Mr. Specter, the ranking Republican on the Senate Judiciary Committee, said on CBS’s “Face the Nation” program. “I want to know what the program is all about. I don’t know if they’ve been telling us the truth or not because I do not know what the program is.”

At issue is an administration briefing on March 10, 2004, for congressional leaders. Mr. Gonzales told the Judiciary Committee this week the subject of the briefing wasn’t what has become known as the terrorist surveillance program. Rather, it dealt with other, related intelligence activities that he declined to describe. Members of Congress who attended the briefing disputed Mr. Gonzales’s version of events.

Senator Schumer, a Democrat of New York, said the “evidence is overwhelming” to justify appointment of a special counsel. “There have been so many instances of the attorney general not telling the truth to the committee,” he said on ABC’s “This Week” program.

White House Press Secretary Tony Snow said last week that Mr. Gonzales’s answers were consistent and that the president still supports the attorney general.

Mr. Specter of Pennsylvania said an administration official called him yesterday to describe the program that is the subject of the dispute and he will receive a more detailed briefing on it tomorrow.

A former deputy attorney general, James Comey, told Congress on May 15 that, when Mr. Gonzales was White House counsel in 2004, he pressured Attorney General Ashcroft to approve an extension of the terrorist surveillance program.

In his testimony July 24, Mr. Gonzales said the subject of his discussion with Mr. Ashcroft wasn’t the surveillance program. It was another matter, which also had been the subject of the 2004 White House briefing for congressional leaders that preceded the hospital visit, he said. The administration says the details of that program are classified.

The “attorney general has said there are two programs, more than the one the president has identified,” Mr. Specter said. “I want to find out if that’s true or not.”

The New York Times reported yesterday that one of the classified programs that sparked a legal debate in 2004 involved “data mining,” searches through massive computer databases, by the National Security Agency that may have captured records of millions of Americans. The NSA also operated the terrorist surveillance program, which has been publicly acknowledged by the administration.

Rep. Jane Harman, a California Democrat and one of eight lawmakers who attended the 2004 briefing, said yesterday that “only one program was at issue” during the meeting.

The suggestion that there were separate programs or that Congress doesn’t know what they are because changes were made is “a very slippery slope,” Harman, who was the senior Democrat on the House Select Committee on Intelligence at the time, said on CNN’s “Late Edition” program. “The chief law enforcement officer needs to tell the truth.”

Senator Leahy, the Vermont Democrat who heads the Judiciary Committee, again urged Mr. Gonzales yesterday to review his testimony, which he was given a week to do, and consult with an attorney on any errors.

“The testimony he gave is not truthful,” Mr. Leahy said on CBS. “I want the truth.”

The Senate Democrats have asked Solicitor General Paul Clement to name a special counsel. Clement is acting attorney general in matters in which Mr. Gonzales has recused himself.

Mr. Specter said yesterday that it’s “premature” to call for a special prosecutor until Mr. Gonzales is given “a chance to correct the record.”

Senator Hatch, a Utah Republican, said on ABC that Democrats are using Mr. Gonzales “as a punching bag to get to the president.”

“We’ve had all this bluster,” Mr. Hatch said. “We’ve had all of these documents. And there isn’t one evidence of impropriety, and yet,” the Democrats “have built this like it’s some sort of a big scandal and it’s not.”