Herman Cain said Sharon Bialek, the first accuser to come public with her allegations against him, was lying about her account and that he didn't "remember knowing her."
He also said the allegations would not force him from the presidential race.
"I can categorically say i have never acted inappropriately with anyone, period," Cain said in an interview Tuesday with ABC News and Yahoo. "As far as these latest charges, I don't even remember - I reject all these charges."
In a press conference Monday and subsequent media interviews on Tuesday, Bialek described, in detail, sexually inappropriate behavior she claims Cain did.
Cain said that while watching her press conference, he struggled to recall having ever met Bialek.
"When I first saw her, I didn't recollect - I didn't even recognize her," Cain said. "I am honestly telling you I can't even recall knowing her back then."
When asked if Bialek was lying, Cain said: "Yes, I’m saying that as nice a way as I can.”
Bialek is the fourth women to make allegations against Cain since the original story broke last week but she is the first to come forward publicly.
Cain, after addressing the original allegations, had taken a quieter approach in dealing with them, letting his campaign issue denials while he stayed out of the press. That changed Tuesday with his interview with ABC. He also plans to hold a press conference at 5 p.m. Tuesday.
He told ABC News that the allegations were taking a toll on his family, especially on his wife Gloria, who he described as "angry" over the situation. But, Cain said, he had no plans to introduce her to the campaign trail in an attempt to bolster his image.
"She was dealing with me running for president quite well until last week, the last couple of days," Cain said. "I want her to continue being that calm and tranquility for our family."
He also said that his wife found Bialek's claims not to be credible after watching her press conference on Monday.
"That stuff doesn't even sound like you, let alone that you did this with someone who is making these accusations," Cain reported his wife to have said.
But, Cain said, while the allegations were frustrating, he was not considering departing the race.
"I am not going to be discouraged to the point that I am going to pull out of this race," Cain said.
His poll numbers have not dipped in polling taken since the story became public. He and Mitt Romney remain at the top of the race for the Republican presidential nomination.
Cain's account sharply contrasts with that of Bialek, who said that Cain tried to grope her after drinks and dinner in July 1997. Bialek also said she confronted Cain at a Tea Party dinner in Chicago within the past couple of months.
But Cain maintained that he did not remember her, or any of the incidents she described.
"I have absolutely not acted inappropriate with this lady or any other," Cain said.
His campaign issued a memo Tuesday attacking Bialek's credibility, detailing what it characterized as Bialek’s “long and troubled” history, including a 1999 paternity dispute, to argue that the public should trust Cain over his latest accuser.
“In stark contrast to Mr. Cain’s four decades spent climbing the corporate ladder rising to the level of CEO at multiple successful business enterprises, Ms. Bialek has taken a far different path,” the Cain campaign said.
Asked by ABC News' Jonathan Karl why four women had come forward to accuse him of harassment, Cain said that he believed that the reports were politically motivated.
"There's an element in this country...that does not want to see a businessman succeed," Cain said. "They really don't want to see an unconventional candidate who is connecting with the people."
Cain was also asked to respond to the comments of another former businessman vying for the Republican nomination - Romney. Earlier Tuesday, Romney described Bialek's allegations as "particularly disturbing" and "serious."
"He's right - they're disturbing to me, they're serious, I've taken them serious," Cain said.
