The White House said in a letter late Thursday to the independent Sept. 11 commission that such a session would allow Condoleezza Rice to clear up "a number of mischaracterizations" of her statements and positions.
Rice, who has spoken frequently and written about the administration's pre- and post-Sept. 11 strategy, still would not testify publicly before the panel, as the members and many relatives of victims of the 2001 terrorist attacks want.
In his letter, White House Counsel Alberto Gonzales wrote that it was important that presidential advisers such as Rice "not be compelled to testify publicly before congressional bodies such as the (Sept. 11) commission."
The White House move follows highly publicized testimony to the commission this week by Richard Clarke, a counterterrorism adviser to the past three presidents and author of a new book critical of Bush.
Clarke, who left his White House post 13 months ago, told the commission on Wednesday that the administration invasion of Iraq undermined the war on terror.when it came to power than the outgoing Clinton administration had shown. He also said the
With Clarke striking at the heart of Bush's re-election strategy, the White House has mounted, accusing the former adviser of seeking to rewrite history to sell copies of his tell-all book.
"He needs to get his story straight," Rice said as the White House identified Clarke as the senior official who had praised Bush's anti-terrorism efforts in an anonymous briefing for reporters in 2002.
Adding new intensity to the flap, Senate Majority Leader Bill Frist said Friday that key Republicans in Congress are seeking to declassify testimony that former terrorism adviser Richard Clarke gave in 2002 about the 9/11 attack.
CBS News Correspondent
It was a highly unusual move, and Frist said the aim was to determine whether Clarke lied under oath — either in 2002 or this week — when he appeared before a bipartisan Sept. 11 commission and sharply criticized Bush's handling of the war on terror.
For his part, Bush defended his handling of the war on terror during a trip to New Hampshire on Thursday, without mentioning Clarke by name.
"Had I known that the enemy was going to use airplanes to strike America, to attack us, I would have used every resource, every asset, every power of this government to protect the American people," the president said.
Public trust in the president's judgment was relatively high after the terrorist attacks on New York City and Washington and spiked up again during the Iraq war. But the percentage of people who trust Bush has fallen below 50 percent in some polls since.
Retracted White House statements do little to boost public trust. CBS News Correspondent
The White House today reversed that comment, and staff members now tell reporters, "We are not denying such a meeting took place. It probably did."
Republican and Democratic members of the Sept. 11 commission have urged the administration to abandon its refusal to allow Rice to testify publicly. Some GOP members of Congress, speaking on condition of anonymity, said they also believed Rice should appear, at least in part to rebut Clarke.
Rice had said Wednesday she was willing to return for another private session. She met privately with panelists for about four hours on Feb. 7.
Her refusal to appear publicly, while at the same time granting a host of nationally broadcast interviews, has produced harsh criticism. On Sunday, Rice was to appear again, this time on CBS' "60 Minutes" a week after Clarke used that program to talk about his book.
Secretary of State Colin Powell will also defense the White House on CBS' Face The Nation, 10 a.m. ET Sunday.
"The American public wants answers to these questions. She ought to testify. She ought to testify under oath," Terry McAuliffe, the Democratic Party chairman, said Friday on ABC's "Good Morning America."
"This is about getting to the bottom of some very serious questions about what went on around Sept. 11 and why we didn't do a better job of preparing ourselves."
McAuliffe's Republican counterpart, Ed Gillespie, countered on the same show that "for a White House staffer to appear before a legislative branch body, that's different than talking to reporters."
The White House said Rice wanted to rebut statements made in this week's public testimony before the panel.
Gonzales also said statements that other national security advisers have testified before Congress in open session were wrong. Previous testimony from national security advisers have either been in closed session or involved potential criminal wrongdoing, Gonzales said.
The commission also has been denied the opportunity to question Bush and Cheney in open session. The White House has agreed to allow those interviews to occur only privately, and only with two commissioners.