Carolyn Kaster, File, Associated Press
FILE - In this Nov. 2, 2011 file photo, Republican presidential candidate Herman Cain arrives to speak on Capitol Hill in Washington. Cain is defending himself anew and _ without evidence _ blaming presidential rival Rick Perry's campaign of being behind the disclosure of years-old sexual harassment allegations against him. Cain is pressing forward, even as a third woman says she considered filing a complaint against him over sexually suggestive remarks and gestures.

WASHINGTON — Republican presidential hopeful Herman Cain struggled to overcome a storm of controversy stemming from sexual harassment accusations on Thursday as the threat of a damaging written statement by one of his accusers and shifting explanations by a top aide left his efforts and even his candidacy in doubt.

"This will not deter me" in the race for the White House, Cain declared as he made a series of appearances on conservative media outlets. He repeatedly denied the accusations and blamed an inside-the-Washington Beltway culture he described as "guilty until proven innocent" for the intense scrutiny.

At the same time, he tried to demonstrate a campaign returning to normalcy. He discussed foreign policy with Henry Kissinger, for example, and held other meetings in New York.

Since the allegations surfaced late last weekend, Cain has said consistently he never sexually harassed anyone, but his answers to other pertinent questions have changed repeatedly. In one instance, he first denied knowing of any financial settlements, then said he recalled one, explaining he had been aware of an "agreement" but not a "settlement."

On Wednesday, Cain said he believed a political consultant for rival Rick Perry had leaked the information. The consultant, Curt Anderson, denied it.

In a television interview on Thursday with Fox News Channel, Mark Block, Cain's chief of staff, first stood by the accusation, then reversed course. "Until we get all the facts, I'm just going to say we accept what Mr. Anderson said."

It was unclear when all the facts might emerge.

Joel Bennett, an attorney for one of the women alleging sexual harassment, said he was seeking permission from the National Restaurant Association to release a statement on her behalf. Under an agreement reached in 1999, the woman agreed not to speak publicly about the episode she said occurred when she worked for the trade group and Cain was its president.

Cain has not said whether he wants his former employer to grant the woman's request. Sue Hensley, a spokeswoman for the restaurant group, said its lawyers were reviewing the draft statement and would respond on Friday.

For the most part, Cain's presidential rivals steered clear of the controversy, preferring to let it play out.

Cain, in an interview with the conservative Daily Caller, said it can be disorienting campaigning in the nation's capital.

"The way questions are asked, when I'm speaking to a group here in D.C. is coming from a totally different perspective than when I'm being asked questions from the real people. The real people come at it, here's the problem, what do you think the solution is?

"Inside D.C., inside the bubble as you call it, they're coming at the perspective of skepticism. ... You can't get it done. You're going to get knocked down. And you can just feel it in the way they ask the question and the way they respond."

Apart from seeking to burnish his credentials as a political outsider, Cain and his allies have also claimed that as a black conservative, he is subject to harshness because of his race.

Whatever the outcome, Cain's spokesman, J.D. Gordon, said the campaign had raised $1.2 million since news of the allegations first surfaced.

The controversy erupted at a time when Cain had vaulted to the top of public opinion polls as a leading conservative challenger to former Massachusetts Gov. Mitt Romney for the Republican nomination.