Alberto Gonzales, with a fresh vote of confidence from President Bush, vowed Monday to remain as attorney general despite lingering differences with senators over the firing of federal prosecutors.

Appearing at a news conference on identity theft, Gonzales said he will remain "as long as I can continue to serve effectively."

"There are a series of priorities, a series of objectives, that I want to see accomplished," he said, "and we are working as hard as we can to achieve those objectives. Obviously, as head of an agency ... we worry about questions about morale. The way I do it is by speaking directly to U.S. attorneys. ... "

"I have an obligation to work with the Congress and I will continue to work with the Congress," he said.

"We're going to correct the mistakes that have been made. I have accepted responsibility," Gonzales said. "I've already indicated that I've made mistakes and I accept responsibility for that."

Bush gave Gonzales a strong vote of confidence on Monday despite scant support and scathing criticism from key Republicans.

"This is an honest, honorable man, in whom I have confidence," Bush said.

On Monday, Bush issued a statement commending Gonzales for his work on the Identity Theft Task Force Report with Federal Trade Commission Chair Deborah Majoras.

"Identity theft is a serious problem in America, and my Administration is working to combat this crime and to assist its victims," said Bush. "I thank the Attorney General, the Chairman, and their staffs for taking on this difficult and important assignment."

The president said that Gonzales' testimony before skeptical Judiciary Committee senators last week "increased my confidence" in his ability to lead the Justice Department. Separately, a White House spokeswoman said, "He's staying."

Gonzales has been under fire for what the White House acknowledges was his poor handling of the firing of eight federal prosecutors. He claimed dozens of times at last week's hearing that he couldn't recall key details about the prosecutors' firings or about a key November meeting that documents show he attended.

Bush said that while some senators did not like the way Gonzales answered the questions, he continues to back his attorney general.

"As the hearings went forward, it was clear the attorney general broke no law, there's no wrongdoing," Bush said.

However, key GOP lawmakers continued to raise doubts about Gonzales.

Sen. Arlen Specter of Pennsylvania, the top Republican on the committee, said on Sunday that 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," Specter said of Gonzales' appearance. "No doubt, it is bad for the Department of Justice. It is harmful. There has been a very substantial decrease in morale."

"All of America saw why so many of us had felt for so long that he shouldn't be attorney general," said Sen. Charles Schumer, D-N.Y., a Judiciary committee member and one of Gonzales' most vocal critics. "He was not in command of the facts. He contradicted himself. And he doesn't really appreciate the role of attorney general."

Schumer maintained that Gonzales ought to step down as soon as possible.

Asked whether Gonzales should resign, Senate Judiciary Committee Chairman Patrick Leahy, D-Vt., said: "I don't think he can be effective" if he remains in office.

Bush spoke about Gonazales during an Oval Office meeting with Gen. David Petraeus, commander of the Iraq war.

"The attorney general went up and gave a very candid assessment, and answered every question he could possibly answer — honestly answer — in a way that increased my confidence in his ability to do the job," Bush said.

White House deputy press secretary Dana Perino said that, "Now there are some people, granted, that don't support the attorney general. But he has the full confidence of the president. We reserve the right to respectfully disagree with friends of ours on Capitol Hill in this regard."

Acknowledging Gonzales' lack of support in Congress, Perino said the Justice Department has "a huge amount of responsibility outside of any dealings with Capitol Hill."

"I think that it was good to get the hearing over with," she said. "People can take a step back and then either ask follow-up questions or move on."

The Associated Press contributed to this report.