WASHINGTON (Reuters) - Republican U.S. lawmakers turned up the heat on Sunday on Susan Rice, saying the U.N. ambassador - seen as a possible nominee to replace Hillary Clinton as secretary of state - must testify before Congress on her remarks after the September attack that killed the American envoy to Libya.

Two influential Senate Republicans, John McCain and Lindsey Graham, did not back down on Sunday from their vow made last week to oppose any attempt by President Barack Obama to put Rice into a Cabinet position that would require Senate confirmation.

"She has a lot of explaining to do. I am curious why she has not repudiated these remarks," McCain, the top Republican on the Senate Armed Services committee, said on CBS's "Face the Nation" program.

Obama last Thursday warned Republicans that if they had a problem with the U.S. handling of the Benghazi attack in Libya to "go after me" rather than picking on Rice.

McCain said he wished the president would not waste time getting mad at him but instead spend the time finding out what happened in Libya and how could it be prevented in the future.

"She's going to have to come in and testify at some point, whether it's in a closed hearing or an open hearing," Republican Saxby Chambliss, vice chairman of the Senate Intelligence Committee, told the "Fox News Sunday" program, referring to Rice.

"We're going to have an open hearing, too. But at some point, she needs to come in and say what the president or the White House directed her to say," Chambliss added.

Republicans have criticized Rice for appearing on Sunday morning news shows five days after the September 11 attack on the U.S. diplomatic mission in Benghazi and saying that preliminary information suggested the assault was the result of protests over an anti-Muslim film rather than a premeditated strike.

The U.S. ambassador to Libya, Christopher Stevens, and three other Americans were killed in an attack that has raised questions about the security of the diplomatic mission, U.S. intelligence about the threat, and the adequacy of the immediate U.S. response.

The White House has said Rice's comments were based on the best information Rice had at the time. Republicans have used her early assessment as a cudgel for criticizing the administration as not being forthcoming about Benghazi. The senators' remarks last week suggested they would pursue the issue even though the U.S. presidential election is over.

'DESTROYS THE NARRATIVE'

Graham said Rice's initial explanation helped reinforce the Obama administration's "narrative" that al Qaeda has been weakened.

"Had the truth come out a few weeks before the election that our consulate in Benghazi had been overrun by an al Qaeda-sponsored, affiliated militia, that destroys the narrative we have been hearing for months that al Qaeda's been dismantled," Graham said on NBC's "Meet the Press" show.

"The truth of the matter is nothing could be further from the truth, and the story she told helped reinforce the political narrative helpful to the president," Graham said. "I don't know what she knew, but I know the story she told was misleading. I don't know why it was misleading." Continued...