In a letter to the commission chairman and vice chairman from counsel Alberto Gonzales, the White House that such a session would allow her to clear up "a number of mischaracterizations of Dr. Rice's statements and positions."
Rice still would not testify publicly before the panel, as the members and many relatives of victims of the 2001 terrorist attacks want. Gonzales wrote that is important that presidential advisers such as Rice "not be compelled to testify publicly before congressional bodies such as the Commission."
Rice had said Wednesday that she was willing to return for another private session with the commission.
"I also have a responsibility to make sure that the commission knows everything that I know, and that's why I spent four hours with them, and I'm prepared to spend longer with them anywhere they want, any time they want, answer as many questions as they have," she told reporters in a briefing. "And I hope we'll have an opportunity to do that. But I just have to maintain the separation."
But the letter from Gonzales to former New Jersey Gov. Thomas Kean, a Republican and the commission chairman, and commission vice chairman Lee Hamilton, a former Democratic congressman from Indiana, represented the White House's formal offer of Rice's return.
In other developments:
The commission's next public hearings, on April 13-14, focus on intelligence failures. CIA Director George Tenet is scheduled to provide additional testimony.
The commission plans private interviews with Clinton and former Vice President Al Gore, but has yet to arrange similar meetings with Bush and Vice President Dick Cheney because they have only agreed to be interviewed by just two commissioners.