Ayotte told CNN after the late November meeting with Rice, Graham, and McCain, "Certainly she misled the American public."
Former CIA Director David Petraeus, who resigned last month after admitting to an extramarital affair, returned to Capitol Hill to testify on the attacks, and Clinton is scheduled to testify next week.
Sen. Susan Collins, the moderate Republican from Maine, said through a spokesman that the Senate Homeland Security Committee, where she serves as ranking member, would continue its investigation into the Benghazi attack. She had raised her own questions about Rice's potential nomination after a private meeting with the ambassador.
The Thursday decision was Rice's own; she was not asked to step aside in the consideration process, a former administration official who had knowledge of her decision said.
"She has got a lot of honor, a lot of dignity, a lot of patriotism. This was a completely manufactured distraction, and she was determined to put her country first," the former official said. "No nominee for secretary of state has been subjected to such a sustained campaign of politicization and slander. And it is really troubling."
Madeleine Albright, who was the first woman to serve as secretary of state and has known Rice for decades, said Rice is "brilliant" and described her withdrawal from consideration as "sad."
"I think it is genuinely, genuinely sad because she is one of the smartest people that I know and completely dedicated to serving the United States," Albright told CNN. Rice "put the country and the president ahead of her own ambition. It just shows what a tremendously thoughtful and good and responsible person she is."
In her letter to Obama, Rice wrote "the position of secretary of state should never be politicized."
"As someone who grew up in an era of comparative bipartisanship and as a sitting U.S. national security official who has served in two U.S. administrations, I am saddened that we have reached this point, even before you have decided whom to nominate," she wrote. "We can not afford such an irresponsible distraction from the most pressing issues facing the American people."
Rice served in President Bill Clinton's administration on the National Security Council, eventually leading African affairs for the council and serving as a special assistant to the president.
She was confirmed by the Senate as the top diplomat to the U.N. in January 2009.
If Rice had been nominated, she would have faced criticism from religious leaders about her role in the Clinton administration's handling of the Rwandan genocide in the 1990s.
U.S. Rep. Mike Rogers, chairman of the Permanent Select Committee on Intelligence, said on CNN that Rice's decision was "probably for the best."
"I think Ambassador Rice was facing an uphill battle in the senate for any confirmation she may have received," he said.
Asked in an interview Thursday on NBC whether she wanted the top diplomatic post, Rice replied that she "would have been very honored to serve in that job."
She added, "But yeah, sure. How can you not want to -- in my field -- serve at the highest possible level?"