"The talking points provided by the intelligence community, and the initial assessment upon which they were based, were incorrect in a key respect: There was no protest or demonstration in Benghazi," Rice said in a statement after the meeting. "While we certainly wish that we had had perfect information just days after the terrorist attack, as is often the case the intelligence assessment has evolved."
She insisted that there was no intention to mislead the American people, and the administration updated Congress as the assessment evolved. The senators, though, were not mollified.
"We are significantly troubled by many of the answers that we got and some that we didn't get concerning evidence that was leading up to the attack on the consulate and the tragic death of four brave Americans and whether Ambassador Rice was prepared, or informed sufficiently, to give the American people the correct depiction of the events that took place," McCain told reporters.
Said Graham: "Bottom line I'm more disturbed now than I was before that 16 September explanation."
The three insisted that they need more information about the Libyan raid before they even consider Rice as a possible replacement for Clinton.
"I'm more troubled today," said Ayotte, who argued that it was clear in the days after the attack that it was terrorism and not a spontaneous demonstration prompted by an anti-Muslim video.
At the White House, spokesman Jay Carney said there were "no unanswered questions about Rice's appearance on the Sunday shows and the talking points that she used that were provided by the intelligence community. Those questions have been answered."
Carney called the focus on Rice's appearance on the Sunday shows an "obsession."
Despite lingering questions over her public comments after the Benghazi attack, Rice has emerged as the front-runner on a short list of candidates to succeed Clinton, with Sen. John Kerry, D-Mass., seen as her closest alternative.
The strong statements from the three senators clouded Rice's prospects only two days after Republican opposition seem to be softening. Rice planned meetings on Wednesday with Sen. Bob Corker of Tennessee, who is in line to become the top Republican on the Foreign Relations Committee, and Sen. Susan Collins, R-Maine.
Corker said Tuesday that he had concerns with a possible nomination.
"When I hear Susan talk she seems to me like she'd be a great chairman of the Democratic National Committee," Corker said. "There is nobody who is more staff supportive of what the administration does. That concerns me in a secretary of state."
Rice's series of meetings on Capitol Hill will be a critical test both for Republicans, who will decide whether they can support her, and the administration, which must gauge whether Rice has enough support to merit a nomination.
A senior Senate aide said the administration was sounding out moderate members of the Senate Foreign Relations Committee, such as Corker and Sen. Johnny Isakson, R-Ga. Assessing the prospects for Rice before Obama makes any announcement would avoid the embarrassment of a protracted fight with the Senate early in the president's second term and the possible failure of the nominee.
Rice is scheduled to meet with Sen. John McCain, R-Ariz., her most vocal critic on Capitol Hill, and Sen. Kelly Ayotte, R-N.H. McCain and Ayotte are members of the Senate Armed Services Committee.
On talk shows the weekend following the attack, which took place on the 11th anniversary of 9/11, Rice was given talking points that described the attack as a spontaneous protest of the film, even though the Obama administration had known for days that it was a militant assault.
Republicans called her nomination doomed, leading to a vigorous defense of her by Obama in his first postelection news conference. Since then, GOP lawmakers have appeared to soften their views. McCain, who said earlier this month that would he do everything in his power to scuttle a Rice nomination, said Sunday that he was willing to hear Rice out before making a decision.
Sen. Jim Inhofe, R-Okla., a member of the Senate Foreign Relations Committee, had issued a statement highly critical of Rice on the day of Obama's news conference. He indicated Monday that perhaps she didn't know what had transpired in Benghazi on the day of the attack.
"I assumed she had full knowledge of everything that went on. I'm not at all convinced of that now. She very well could have been thrown under the bus," Inhofe said in an interview. He said she hadn't requested a meeting but he would be glad to meet with her.
White House spokesman Jay Carney said Monday that the administration appreciated McCain's latest comments about Rice, but wouldn't say whether the president saw them as an opening to make the nomination. "Ambassador Rice has done an excellent job at the United Nations and is highly qualified for any number of positions," Carney said.
Several diplomats currently serving with Rice said that what she lacked in Clinton's star power, she could make up with a blunter approach that demands attention and has marked her tenure thus far at the United Nations.
Rice, who at 48 is relatively young, has been known to covet the job for years, but was passed over for Clinton in 2009.
Associated Press writers Matthew Lee in Washington and Edith M. Lederer in New York contributed to this report.