By Tabassum Zakaria

WASHINGTON (Reuters) - U.S. Ambassador to the United Nations Susan Rice on Tuesday failed to win over her harshest Republican critics in the U.S. Senate who are threatening to block her nomination if President Barack Obama chooses her for Secretary of State or another top post in his second-term Cabinet.

Rice met for about an hour behind closed doors at the U.S. Capitol with Senators John McCain, Lindsey Graham and Kelly Ayotte. They have openly criticized her for initial comments after the September 11 attack on the U.S. mission in Benghazi that suggested it was a spontaneous event arising from protests of an anti-Islam film rather than a preplanned terrorist strike.

The U.S. ambassador to Libya and three other Americans were killed in the attack on the Benghazi mission and a nearby CIA annex. Intelligence officials later said the attack was possibly tied to al Qaeda affiliates.

"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.

Rice was accompanied by a CIA official and was not seen by reporters.

President Barack Obama has defended Rice and said if senators had a problem with her comments on a round of Sunday television talk shows days after the attack, they should go to him.

(Reporting by Tabassum Zakaria; Editing by Jackie Frank)