WASHINGTON — Attorney General Gonzales has hurt the Bush administration and the Department of Justice with his poor handling of the firing of eight federal prosecutors, a leading Republican said yesterday.

The top Republican on the Senate Judiciary Committee, Senator Specter, said Mr. Gonzales was certainly undermining himself and his agency’s law enforcement efforts.

“The attorney general’s testimony was very, very damaging to his own credibility. It has been damaging to the administration,” Mr. Specter said of Mr. Gonzales’s appearance before the Senate Judiciary Committee this past week. “No doubt, it is bad for the Department of Justice. It is harmful. There has been a very substantial decrease in morale.”

Mr. Specter stopped short of adding his name to the growing ranks of lawmakers calling on Mr. Gonzales to resign. “I don’t challenge anybody else who wants to do it,” Mr. Specter said. “My own mindset is to leave it up to the attorney general and the president.”

“All of America saw why so many of us had felt for so long that he shouldn’t be attorney general,” a judiciary committee member and one of Mr. Gonzales’s most vocal critics, Senator Schumer, said. “He was not in command of the facts. He contradicted himself. And he doesn’t really appreciate the role of attorney general.” Mr. Schumer maintained yesterday that Mr. Gonzales ought to step down as soon as possible.

Asked whether Mr. Gonzales should resign, the Democratic chairman of the Senate Judiciary Committee, Senator Leahy, said. “I don’t think he can be effective” if he remains in office.

“A lot of those calls are coming from Republicans,” Mr. Leahy added. “He’s lost the confidence of many Democrats and Republicans in the Congress, and many people throughout America.”

Some give Mr. Gonzales a chance of getting past the flap. “I think he can survive,” a member of the judiciary committee and GOP presidential hopeful, Senator Brownback, said. Mr. Gonzales has “got difficulties, he’s got problems,” Mr. Brownback said.