"This will not deter me" in the race for the White House, Cain declared, repeatedly denying the accusations 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 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.
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 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 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 also 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."
For the most part, Cain's presidential rivals steered clear of the controversy, preferring to let it play out.
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.
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."
Associated Press writers Steven Ohlemacher, Brett Blackledge and Laurie Kellman contributed to this story.