"Here we go again. I didn't do anything wrong," Cain said in a pre-emptive denial that lumped a detailed claim of a consensual affair in with earlier allegations of sexual harassment.
But the woman, Ginger White, said in an interview with Fox 5 Atlanta that over the years, Cain bought her airplane tickets so she could join him in cities as far-flung as Palm Springs, Calif., and Atlanta.
"It was fun," the 46-year-old White said. "It was something that took me away from my humdrum life at the time. And it was exciting."
Cain's candidacy was soaring in the polls until he was hit less than a month ago with accusations that he sexually harassed several women and groped one while he was a high-ranking official at the National Restaurant Association. He has since fallen back in the public opinion surveys, and been eclipsed by former House Speaker Newt Gingrich in the race to emerge as the principle conservative alternative to Mitt Romney.
At her apartment in Dunwoody, Ga., White declined to elaborate on her statements during a brief interview with AP. "I can't make any comment on this," she said. "We're trying to be slightly sensitive."
In its report, the television station said White had Cain's name in her cell phone contacts, and when its reporter sent a text message to the number, he called right back.
"He told us he knew 'Ginger White' but said he was trying to help her financially," the station said.
In a written statement released immediately after the story aired, Cain's campaign said detractors were trying to "derail the Cain Train with more accusations of past events that never happened."
Later, at a fundraiser in the Virginia suburbs of Washington, D.C., Cain avoided reporters' questions.
In his initial denial, televised on CNN, Cain vowed to remain in the presidential race, as long as he has the support of his wife, with whom he said he had discussed the most recent allegation.
In her interview, White said she decided to come forward after seeing Cain attack his other accusers in an appearance on television.
"It bothered me that they were being demonized, sort of, and being treated as if they were automatically lying, and the burden of proof was on them," she said. "I felt bad for them."
White told the Atlanta TV station she expects to be scrutinized by Cain and the media.
Georgia court records show a series of judgments against White for not paying rent in Atlanta area apartments, including one filed about two weeks ago.
In the interview, she said she first met Cain in the late 1990s in Louisville, Ky., when he was president of the National Restaurant Association. They had drinks and he invited her to his hotel room, she recalled.
She quoted Cain as telling her, "You're beautiful to me and I would love for us to continue this friendship," then produced his personal calendar and invited her to meet him in Palm Springs.
In this case, unlike the others, Cain took the unorthodox step of issuing a denial in advance.
"I did not have an affair, and until I see and hear exactly what's going to be, what accusations are going to be made, let's move on," he said.
Asked if he suspected his accuser had emails, letters, gifts or other possible evidence of an affair, he replied,"No."
In a statement provided to AP, Cain's lawyer, Lin Wood, said the former businessman has no obligation to "discuss these types of accusations publicly with the media and he will not do so even if his principled position is viewed unfavorably by members of the media."
The statement drew a distinction between "private alleged consensual conduct between adults" and a case of harassment. It did not include an explicit denial of an affair along the lines that Cain himself provided in his television interview.
Contacted by AP, Wood added, "If any candidate wants to publicly discuss his private sex life, that is his or her life. But I don't believe that there's an obligation on the part of any political candidate to do so."
White's attorney, Edward Buckley, did not immediately return messages seeking comment.
Ray Henry reported from Atlanta. Associated Press writer Greg Bluestein contributed to this report from Atlanta.