The White House agreed Tuesday to let National Security Adviser Condoleezza Rice (search) publicly testify under oath before the commission investigating the Sept. 11 attacks on the United States.

In return, the National Commission on Terrorist Attacks on the United States (search) unanimously agreed to a Bush administration request that Rice's testimony will not set a precedent that would require future White House aides to publicly testify.

In a letter to the commission sent Tuesday by White House Counsel Alberto Gonzales (search), the White House asserted that any testimony by Rice "can occur only with recognition that the events of September 11, 2001 present the most extraordinary and unique circumstances.

"Nevertheless, the president recognizes the truly unique and extraordinary circumstances underlying the commission's responsibility to prepare a detailed report on the facts and circumstances of the horrific attacks on September 11, 2001," Gonzales wrote.

Click to read the letter from White House Counsel Alberto Gonzales.

The decision comes after a tumultuous week in Washington, during which the White House was pressured by Democrats and Republicans alike to allow Rice to testify publicly and under oath.

The Sept. 11 commission wants to question her about what counterterrorism meetings and strategy discussions she was privy to in the days leading up to and following the devastating Al Qaeda attack in 2001.

Several commission members pointedly mentioned her absence at last week's hearings — particularly when they questioned Deputy Secretary of State Richard Armitage.

The White House's letter also offered to let President George W. Bush and Vice President Dick Cheney to meet jointly with the entire commission, though they would not be under oath. Bush and Cheney, as well as former President Bill Clinton and Vice President Al Gore, previously agreed to meet with the commission.

Bush planned to address the Rice decision Tuesday, after an appearance in Appleton, Wis.

"The White House is committed to providing all the information they need," press secretary Scott McClellan told reporters.

The 10-member bipartisan commission issued a statement praising the decision and agreeing with the White House's interpretation of how Rice's testimony should be viewed.

"We agree with the observation by the president's counsel that Dr. Rice's appearance before the Commission is in response to the special circumstances presented by the events of September 11 and the Commission's unique mandate and should not be viewed as a precedent for future requests for public testimony by White House officials," the statement said.

Click to read the statement from the Sept. 11 commission.

The commission's Republican chairman, former New Jersey Gov. Thomas Kean (search), welcomed the decision and said the White House shouldn't be concerned that the testimony would violate the principles of executive privilege or separation of powers.

"We recognize the fact that this is an extraordinary event. There are all sorts of reasons why this is different. This does not set a precedent," he told reporters. He said there was still no time set — either for Rice's public testimony or for Bush and Cheney's private appearance.

Commissioner Slade Gorton (search), a former Republican senator from Washington, said the Sept. 11 panel accepted the proposal in a meeting Tuesday morning, including the stipulation that it not call other White House officials because "we hadn't planned to."

"I think the White House would have been better off if it had made the agreements sooner, but I'm delighted," said Gorton. "I have felt all along that her public testimony would be good for the country."

Commissioner Bob Kerrey (search), a former Democratic senator from Nebraska, said the president and vice president will not be under oath in their meeting with the commission. Kerry said Rice's testimony will be critical in determining what the Bush administration could have done to prevent the attacks and that the White House "made the right decision."

Rice has already appeared for four hours in front of the commission to answer questions in private when she wasn't under oath about what the administration had been doing about terror threats prior to Sept. 11.

Initially Rice rejected testifying in public, arguing that she was prevented by executive privilege (search) from revealing confidential conversations. She later clarified that she wanted to testify, but couldn't because of the president's concerns that her testimony would violate the separation of powers.

Some legal scholars and partisans have been saying that Rice's discussions in the media about her decision not to testify and the Bush administration's Sept. 11 plans undermined her argument of executive privilege.

"From a political standpoint, it's probably a wise move," said former Republican National Committee Chairman Frank Fahrenkopf (search) of Rice's now-forthcoming testimony. He said that the "fact of 9/11, maybe perhaps an equal of Pearl Harbor" gave the public and the commission the need "for closure," which could be achieved by hearing from all the officials who worked on counterterrorism prior to the tragedy.

Bush aides say the president decided over the weekend to find a way for the national security adviser to go before the commission. The White House wants to respond to claims by former Bush and Clinton counterterrorism coordinator Richard Clarke (search) that the current administration didn't treat the Al Qaeda threat urgently enough.

In addition to possibly dispelling some of the characterizations made by Clarke — who told the commission last week and wrote in a recently published book that the current White House hadn't treated the threat from Al Qaeda (search) with enough urgency — Rice's appearance is likely to blunt attacks from other quarters.

Democrats, meanwhile, said the White House decision was a good start, but didn't address all their concerns.

"The Bush administration has finally come to its senses on what should have been a simple issue by reversing its previous refusal to allow the national security adviser to testify in public under oath," said House Democratic Leader Nancy Pelosi. "The Bush administration needs to understand that the independent 9/11 commission seeks truth, not blame."

Democratic senators on Tuesday had planned on offering a resolution in the form of an amendment to the welfare reauthorization bill that would have required Rice to testify in public and under oath.

The resolution, offered by Sens. Charles Schumer (search) of New York and Edward Kennedy (search) of Massachusetts, was going to demand that Rice testify in order to "make a full accounting of the preparedness of the United States before, and the response of the United States to, the September 11, 2001, attacks."

"I would remind the president what all Americans know: The truth will set you free," Schumer said in a statement after the White House's decision became public. "The administration's reversal shows that it was using executive privilege as an excuse to keep Dr. Rice from testifying. But the dedication and bull's eye integrity of the commission has succeeded and now hopefully we will be a lot closer to the truth."

Fox News' Wendell Goler, Jim Angle, Sharon Kehnemui and Catherine Donaldson-Evans as well as The Associated Press contributed to this report.