"This will not deter me" in the race for the White House, Cain declared, repeatedly denying the allegations in interviews on conservative media outlets.
"Did you tell a woman she looked good?" radio host Sean Hannity asked. "That dress looks hot?"
"Any flirtation that you can think of?"
"Nope," Cain said firmly.
At the same time, he and aides tried to demonstrate a campaign returning to normalcy or even benefiting from the controversy. Cain, a career businessman, held private meetings in New York during the day, including one on foreign policy with former Secretary of State Henry Kissinger.
And campaign spokesman J.D. Gordon said donors had sent in $1.2 million since news of the allegations first surfaced, far above the customary amount for several days.
In a personal note, Cain said his wife, Gloria, was "still 200 percent supportive of me in this whole race, 200 percent supportive of me as her husband, because I haven't done anything." The furor 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 - adding spice to a race already as unpredictable as any in recent memory.
Since it was reported late Sunday that at least two women had complained about Cain when they worked at the National Restaurant Association - and had received financial settlements - Cain has said consistently he never sexually harassed anyone. But his answers to other pertinent questions have changed. In one instance, he first denied knowing of any settlements with former employees, 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 on his 2004 Senate campaign who now is helping presidential rival Rick Perry had leaked the information. But he backed off on the day after. "If he didn't ask me about this and he was my general political consultant, then he didn't do his job," Cain said, referring to Curt Anderson. "I am almost certain that I did" tell him about an allegation.
Anderson denied leaking the information and said he first saw the accusations in the Politico report that started the week's events.
Texas Gov. Perry, who fell in opinion polls as Cain rose, also repeated denials that his campaign had anything to do with the reports. He said on CNN, "This is over, it's gone, it's done with and I'm pressing on."
Media coverage continued. Politico, citing anonymous sources, reported that one of the women contended that Cain made a sexual overture to her and invited her to his hotel room during a National Restaurant Association event in the late 1990s. The report said the woman was livid and complained to a member of the group's board later that night.
The publication cited multiple sources, including an acquaintance of the woman and a person who attended the restaurant association meeting at which the woman lodged her complaint.
In a television interview on Thursday with Fox News Channel, Mark Block, Cain's chief of staff, first stood by his accusation that consultant Anderson first leaked details, then he 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 stemming from her accusation 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.
Asked whether he would like his former employer to agree to the request, Cain sidestepped.
"That's totally their decision," he said on Hannity's program. "I can't ask them to do that because that would create a legal liability that I don't want to be responsible for." Sue Hensley, a spokeswoman for the restaurant group, said its lawyers were reviewing the draft statement and would respond on Friday.
Cain specifically denied allegations by a third woman who told The Associated Press this week that she had considered filing a workplace complaint against him alleging aggressive and unwanted behavior, including a private invitation to his corporate apartment.
He criticized a pollster who did work for the restaurant association when he worked there as politically hostile to him. The pollster, Chris Wilson, said in an interview with AP this week that he witnessed Cain making inappropriate comments and gestures toward a different young woman who worked for the group. He said the event occurred at a dinner in a hotel in Arlington, Va., in the late 1990s.
Cain's presidential rivals generally steered clear of the controversy, preferring to let it play out without offering an opinion on the charges.
"The voters won't find surprises with me. My policy positions have been nothing if not consistent," Rep. Michele Bachmann told Fox News while campaigning in Iowa on Thursday. "I'm not going to comment. It's up to the voters."
Rep. Tom Price, a member of a Georgia delegation that met with Cain earlier in the week, said he's waiting for the details to shake out.
"It's like predicting the end of a football game at the halftime," said Price. "You can't do it."
In one of his interviews during the day, Cain told the conservative Daily Caller 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. After listening to Hannity play recordings of vociferous critics, Cain said, "I'm a black conservative, and it is causing their heads to explode."
Late Thursday, a super PAC called Americans for Cain released a Web video blaming liberals - without offering proof - for the furor surrounding Cain. The 1-minute ad argues that liberals and the mainstream media can't challenge Cain on the merits of his policies, so they've attacked him with the sexual harassment reports, just as Clarence Thomas came under scrutiny for sexual harassment during his Supreme Court confirmation hearings. The ad finishes with nearly 30 seconds of Thomas castigating the Senate Judiciary Committee for considering the allegations and calling the process a "high-tech lynching."
Associated Press writers Steven Ohlemacher, Brett J. Blackledge and Laurie Kellman contributed to this report.