On Capitol Hill, the top Senate Republican called for a review of whether an administration critic lied under oath.
In a letter late Thursday to the commission probing the 2001 terrorist attacks, the White House said it would allow Rice to meet privately for a second time with the panel in order to clear up "a number of mischaracterizations" of her statements and positions during hearings this week.
Rice still would not testify publicly before the panel, as the members and many relatives of victims of the 2001 terrorist attacks want. The White House says presidential aides like Rice cannot be forced to testify before Congress.
The White House also offered Rice to CBS News' 60 Minutes, after the program asked for someone to comment on the week's events. An interview will be taped on Saturday.
In two days of hearings this week, the National Commission upon Terrorist Attacks Against the United States released reports critical of both the Clinton and Bush administration's efforts to defeat al Qaeda before the 2001 attacks.
But one witness, former counterterrorism director Richard Clarke, singled out the Bush team for criticism.
In a highly unusual move, key Republicans in Congress are seeking to declassify testimony Clarke gave in 2002 about the Sept. 11 terrorist attack, Senate Majority Leader Bill Frist said Friday.
Frist said the intent was to determine whether Clarke lied under oath — either in 2002 or this week. He said he personally didn't know whether there were any discrepancies between Clarke's two appearances.
One Republican aide, who spoke on condition of anonymity, said the request had come from House Speaker Dennis Hastert and Rep. Porter Goss, the chairman of the House intelligence committee.
The Sept. 11 commission reported that both the Clinton and Bush administrations pursued mainly diplomatic and legal means to fight al Qaeda that ultimately failed. The panel also saw confusion over whether the CIA had authority to kill bin Laden.
from both administrations testified that wider military action was not feasible before Sept. 11 because of a lack of support from the American people — and may not have prevented the Sept. 11 attacks. Even Clarke, when asked, indicated that nothing the Bush team failed to do would have thwarted the attacks.
But Clarke, who was a counterterrorism adviser to the past three presidents before leaving his White House post 13 months ago, told the commission on Wednesday that the administrationwhen it came to power than the outgoing Clinton administration had shown.
He also said the invasion of Iraq undermined the war on terror.
The panel, in its preliminary reporting, said that prior to Sept. 11, Clarke never me with Mr. Bush about terrorism, a contrast to his time under President Clinton.
Criticism of the president's handling of national security strikes at the heart of Mr. Bush's re-election strategy. The White House has, accusing Clarke of seeking to rewrite history to sell copies of his tell-all book (which is being published by a company that, like CBSNews.com, is owned by Viacom).
"He needs to get his story straight," Rice said as the White House identified Clarke as the senior official who had praised Mr. Bush's anti-terrorism efforts in an anonymous briefing for reporters in 2002.
Mr. 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 Mr. Bush has fallen below 50 percent in some polls since.
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.
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."
Her refusal to appear publicly, while at the same time granting a host of nationally broadcast interviews, has produced harsh criticism.
"This isn't about Condi Rice or executive privilege," Terry McAuliffe, the Democratic Party chairman, said Friday on ABC. "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."