WASHINGTON -- UN Ambassador Susan Rice continued her fight Wednesday to win over skeptics in the Senate who could block her chances at becoming the next U.S. secretary of state, while Republican lawmakers said they were even more troubled after face-to-face meetings with her over the handling of the Sept. 11 deadly attack on the U.S. Consulate in Benghazi, Libya.

Hillary Rodham Clinton is soon expected to step down as secretary of state, and Rice is seen as the top candidate for President Barack Obama to nominate for the post.

Rice on Wednesday was meeting with Republican Sens. Susan Collins and Bob Corker, who is next in line for the top Republican spot on the Senate Foreign Relations Committee.

Rice on Tuesday met behind closed doors with Republican Sens. John McCain, Lindsey Graham and Kelly Ayotte about her much-criticized initial public explanations about the cause of the September attack in Libya that killed Ambassador Chris Stevens and three other Americans.

Her unusual visit to Capitol Hill -- typically, only nominees meet privately with lawmakers -- reflects the Obama administration's support for her efforts.

Rice conceded to the senators that her initial account five days after the attack -- that a spontaneous demonstration over an anti-Muslim video produced in the U.S. triggered it -- was wrong, but she insisted she had not been trying to mislead the American people.

"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 was joined in the meeting by Acting CIA Director Michael Morell.

The senators came out of the meeting indicating they would still try to block Rice's nomination.

"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," McCain told reporters after a session with Rice that he described as candid.

The White House remained defiant in its support for Rice, arguing that she had no responsibility in compiling the information on the cause of the attack.

"The focus on, some might say, obsession on comments made on Sunday shows seems to me, and to many, to be misplaced," Obama spokesman Jay Carney told reporters at a White House briefing.

House Democrats have suggested that the Republican opposition to Rice, a black woman, is sexist and racist.

Corker told The Associated Press before his meeting with Rice on Wednesday, "I think most of us hold the secretary of state and secretary of treasury to a whole different level. We understand that they're going to support the administration, but we also want to know that they are independent enough, when administration is off-base, that they are putting pressure. I think that's what worries me most about Rice."