In a written statement released by the White House, Mr. Bush said his action came at Miers' request.
A White House spokesman denied the president was giving in to pressure from conservatives who vehemently opposed Miers' nomination, but Democrats accused Mr. Bush of bowing to the "radical right wing of the Republican Party."
In a letter to Mr. Bush, Miers, who serves as the president's White House counsel, said, "I am concerned that the confirmation process presents a burden for the White House and our staff that is not in the best interests of the country."
Mr. Bush said he understands and shares Miers' concern. He blamed her withdrawal on calls in the Senate for the release of internal White House documents that the administration has insisted were protected by executive privilege.
Read Harriet Miers' letter to the president (.pdf)
"It is clear that senators would not be satisfied until they gained access to internal documents concerning advice provided during her tenure at the White House disclosures that would undermine a president's ability to receive candid counsel," Mr. Bush said.
"Harriet Miers' decision demonstrates her deep respect for this essential aspect of the constitutional separation of powers and confirms my deep respect and admiration for her."
Miers' surprise withdrawal stunned Washington on a day when the capital was awaiting news on another front – the possible indictment of senior White House aides in the CIA leak case.
CBS News chief White House correspondent John Roberts reports Miers telephoned the president Wednesday night at 8:30 p.m. to say she wanted to withdraw. She delivered her resignation letter to him shortly after 8:30 a.m. Thursday in the Oval Office.
In her letter to Mr. Bush, Miers noted that members of the Senate had indicated their intention to seek documents about her service in the White House in order to judge whether to support her nomination to the Supreme Court.
"I have been informed repeatedly that in lieu of records, I would be expected to testify about my service in the White House to demonstrate my experience and judicial philosophy," she wrote.
"While I believe that my lengthy career provides sufficient evidence for consideration of my nomination, I am convinced the efforts to obtain Executive Branch materials and information will continue."
Miers' nomination has been under withering criticism ever since Mr. Bush announced her selection on Oct. 3. There were widespread complaints about her lack of legal credentials, doubts about her ability and assertions of cronyism because of her longtime association with Mr. Bush.
Mr. Bush's conservative backers had doubts about her ideological purity, while Democrats had little incentive to help the nominee or the embattled GOP president.
Arlen Specter, the Republican chairman of the Senate Judiciary committee, said the way Miers was treated was "disgraceful." The Senate's Democratic leader, Harry Reid, one of the few Democrats who supported Miers, said this was a victory for the "radical right wing" of the Republican Party.
Though not a single Republican senator had announced he would vote against Miers, CBS News correspondent Bob Fuss reports they weren't lining up behind her either. And behind the scenes they were making clear to the White House they didn't want to vote for someone who made the party conservatives so unhappy.
Mr. Bush said that despite her withdrawal, Miers would remain as White House counsel. He did not indicate when he would name a successor.
"My responsibility to fill this vacancy remains," Mr. Bush said in his statement. "I will do so in a timely manner."
Before Mr. Bush chose Miers on Oct. 3, speculation focused on Miers and two other Bush loyalists: Attorney General Alberto Gonzales, a longtime Bush friend who would be the first Hispanic on the court; and corporate lawyer Larry Thompson, who was the government's highest ranking black law enforcement official as deputy attorney general during Mr. Bush's first term.
Other candidates mentioned frequently included conservative federal appeals court judges J. Michael Luttig, Priscilla Owen, Karen Williams, Alice Batchelder and Samuel Alito; Michigan Supreme Court justice Maura Corrigan; and Maureen Mahoney, a well-respected litigator before the high court.