WASHINGTON (CNN) -- President Bush on Monday said he reluctantly accepted the resignation of Attorney General Alberto Gonzales, whose "good name was dragged through the mud for political reasons."

Alberto Gonzales and his wife, Rebecca, have lunch with President and Laura Bush at the Bush ranch Sunday.

After months of standing by his top prosecutor and "close friend," Bush spoke briefly in Texas to praise Gonzales, saying the attorney general endured "unfair treatment that has created harmful distraction at the Justice Department."

Bush said it's "sad that we live in a time when a talented and honorable person" is impeded "from doing important work."

Solicitor General Paul Clement will serve as acting attorney general, Bush said, until a nominee has been confirmed by the Senate.

Earlier in Washington, Gonzales announced his resignation, saying, "I have lived the American dream."

The first Latino to helm the Justice Department said his "worst days as attorney general have been better than my father's best days." Watch Gonzales on his "worst days" as top prosecutor »

Gonzales described public service as "honorable and noble" and thanked Bush for his friendship.

"Yesterday I met with President Bush and informed him of my decision to conclude my government services as attorney general of the United States effective September 17."

Neither Bush nor Gonzales took questions from reporters.

Some senior administration officials floated Homeland Security chief Michael Chertoff as a possible replacement, but others waved CNN away from Chertoff, saying that his nomination could run into problems because of his role during Hurricane Katrina.

A congressional source familiar with deliberations about Gonzales' replacement told CNN that the successor will not be Chertoff and that senior administration officials are "playing you guys," referring to the media.

A source close to Chertoff said of a possible nomination, "this would be a surprise to Mike."

New York Sen. Charles E. Schumer, a Democratic member of the Senate Judiciary Committee, also suggested that a Chertoff confirmation hearing would be contentious.

"I would say there are a lot of questions about Michael Chertoff that will have to be answered." Schumer said. "I wouldn't say yes; I wouldn't say no. It's an open book. It's possible, but its hardly a slam dunk. There are some names who could be a slam dunk."

Schumer, one of Gonzales' chief critics, appealed to the administration "to work with us to nominate someone whom Democrats can support and America can be proud of."

Sen. Arlen Specter of Pennsylvania, the ranking Republican on the Judiciary Committee who has criticized Gonzales' leadership of the Justice Department, called his resignation "a major helpful turn of events."

Specter suggested current or former senators, or someone well-known to the committee would be a good nominee to replace Gonzales.

"There has to be somebody with very solid professional qualifications, somebody who's an experienced lawyer and has demonstrated the kind of judgment that the attorney general is called upon to display," Specter said.

A senior administration official "aware of discussions" said White House Chief of Staff Josh Bolten is looking for a Washington establishment-type, in the model of Treasury Secretary Henry Paulson and White House counsel Fred Fielding.

Another name that emerged is Larry Thompson, a former deputy attorney general who currently serves as vice president and general counsel for PepsiCo. But a spokeswoman for the company said, "We are very fortunate and pleased, but he is very happy in his role here."

According to senior administration officials, when Thompson has been approached in the past to return to the government he has turned down offers, saying he is happy in the private sector.

Aides at the highest level and other top officials received no warning about the Gonzales announcement, Justice Department sources told CNN. They were not informed until a meeting Monday morning, sources said, when Gonzales acknowledged he would be reading a statement later in the day.

Although Bush had long stood by Gonzales, many members of Congress from both sides of the aisle had called on him to quit after the firing of several U.S. attorneys in 2006 -- terminations which were alleged to have been politically motivated.

Senior Justice Department officials say Gonzales' resignation is not expected to affect the scope or pace of an ongoing internal investigation into the U.S. attorneys' dismissals and other issues.

"Alberto Gonzales was never the right man for this job," said Senate Majority Leader Harry Reid on Monday. "He lacked independence, he lacked judgment and he lacked the spine to say no to Karl Rove." Rove, another longtime Bush official and his top political adviser, also resigned this month.

"This resignation is not the end of the story," Reid warned. "Congress must get to the bottom of this mess and follow the facts where they lead, into the White House."

Throughout Gonzales' time as attorney general, controversies surrounded his positions on issues such as U.S. interrogation techniques and the wiretapping of conversations between Americans and suspected terrorists overseas.

In the probe into the U.S. attorney firings, the Senate Judiciary Committee looked into whether the administration may have fired some or all of the U.S. attorneys for political reasons. In his testimony before the committee on multiple occasions, Gonzales repeatedly seemed to contradict himself, other members of his department or Justice Department documents.

Gonzales also was at the center of a dispute over the controversial no-warrant eavesdropping program authorized by Bush and his testimony that there was no dissent among administration officials over the program. Gonzales later sent a letter to Senate leaders acknowledging he "may have created confusion" in his testimony. E-mail to a friend

CNN's Suzanne Malveaux, John King, Dana Bash, Jeffrey Toobin and Terry Frieden contributed to this report.

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