"We want to understand the nature of the decision-making in the highest levels of government," commission chairman Thomas Kean said after the White House — under intense pressure — reversed course Tuesday and agreed to let Rice, who is Mr. Bush's national security adviser, testify publicly.
Administration officials said it was likely that Rice's appearance would come at the end of next week.
Mr. Bush said Tuesday that Rice's appearance would give the nation "a complete picture" of the events in the months and years leading up to the 2001 terror attacks.
"I've ordered this level of cooperation because I consider it necessary to gaining a complete picture of the months and years that preceded the murder of our fellow citizens on Sept. 11, 2001," Mr. Bush said.
The nation "must never forget the loss or the lessons of Sept. 11 and we must not assume the danger has passed," Mr. Bush said in.
CBS News Chief Whitehouse Correspondent John Roberts reports the Bush administration
Politics aside, Rice's appearance could help write the official history of what preceded the attacks. It will also be a major battle in the personal war between Rice and a former counterterrorism official.
Presented with differing accounts of how the government approached terrorism pre-Sept. 11, the commission will be exploring in the midst of a presidential campaign who is more believable — the Bush administration or its critics.
Mr. Bush's former counterterrorism chief, Richard Clarke, contends the president had been.
Turning aggressively public, Rice fired back in a series of interviews such as heron Sunday in which she declared, "I don't know what a sense of urgency — any greater than the one that we had — would have caused us to do differently."
The commission made clear that Rice's assertions in her media interviews will be fair game for their inquiry.
"It's not necessarily … what Condi Rice said to us in the four or five hours we had with her" in a private interview early this year, Kean told reporters. "Sometimes it's some of the things she said to all of you.
"We're going to try and clear up the discrepancies as best we can," said Kean. "Some of those questions may be important to the fact-finding of our report. And obviously we will in our hearing go to some of those questions."
Rice's public accounts of the Bush administration's anti-terrorism preparations have not always been consistent with statements by others in the Bush team, and sometimes she has seemed to be at odds with herself.
— contained in a book published by a company owned by Viacom, which also owns CBSNews.com — has varied, too.
Last week, for example, the White House questioned Clarke's claim in his book that he met Mr. Bush and others in the Situation Room the day after the terrorist attacks, and that the president pressed for any shred of evidence that Iraq was behind the hijackings.
White House spokesman Scott McClellan said Mr. Bush "doesn't have any recollection" of such a meeting or conversation on Sept. 12, 2001, and "there's no record of the president being in the Situation Room on that day."
Later, Rice said Mr. Bush did speak with Clarke that day and, as she put it, asked "did Iraq have anything to do with this?"
Rice also said the Bush administration did not get a plan from the outgoing Clinton administration to deal with al Qaeda. Later, she said Clarke gave the Bush team a "set of ideas" on that subject.
Writing in The Washington Post last week, Rice said the national security team put together a strategy in the spring and summer of 2001 to eliminate al Qaeda, and this included "sufficient military options" to unseat Afghanistan's Taliban government, host of the terrorist network.
But in his testimony to the commission, Deputy Secretary of State Richard Armitage described the strategy as one lacking a ready military posture.
Rice's voice is not the only one that will be heard on the contentious issues of what happened before Sept. 11.
The commission recently contacted President Clinton's presidential library, where federal archivists spent three months gathering 6,000 documents which they turned over to the investigation.
The commission also plans to schedule a joint private interview with President Bush and Vice President Dick Cheney.
Mr. Bush and Cheney had previously offered to meet with only with Kean and vice-chairman Lee Hamilton. The White House changed course, offering to let the president and vice president meet with the full panel, in the same letter where it volunteered Rice for public testimony under oath.
In that letter, sent from White House counsel Alberto Gonzales to the commission, the administration insisted that Rice's appearance does not set a precedent for the appearance of presidential advisers before investigative bodies. Another condition was that the commission seek no other White House official's testimony.