"We are significantly troubled by many of the answers that we got, and some that we didn't get, concerning evidence that was overwhelming leading up to the attack on our consulate," McCain told reporters after the meeting.
"It is clear that the information that she gave the American people was incorrect when she said that it was a spontaneous demonstration triggered by a hateful video," he said.
"It was not, and there was compelling evidence at the time that that was certainly not the case, including statements by Libyans as well as other Americans who are fully aware that people don't bring mortars and rocket-propelled grenades to spontaneous demonstrations," McCain said.
Graham said he would move to block the nomination of "anybody" who was linked to the Benghazi events.
Republicans have argued that the Obama administration tried to play down the terrorist angle in its initial comments to avoid undermining the president's claims of success in fighting al Qaeda in the run-up to the Nov. 6 election.
Rice, who was accompanied to the meeting by acting CIA Director Michael Morell, later issued a statement.
"We explained that 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," she said in the statement.
"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 said.