An Atlanta woman said Monday that she engaged in an extended consensual affair with Herman Cain that began after a business meeting in the 1990s, continued as he flew her from city to city for dates and ended eight months ago — as Cain launched his presidential campaign.

In an interview with Fox News in Atlanta, Ginger White offered details of what she said was a 13-year relationship with Cain, sharing cellphone records that showed repeated calls and text messages from a number she said belongs to the presidential contender.

Cain denied the accusations. In an interview that aired before White’s allegations were broadcast, Cain told CNN’s Wolf Blitzer that he knows White and that the two had been friends but that there had been no sexual contact and no “affair.” He characterized their relationship as “trying to help a friend” because of her “not having a job etcetera and this sort of thing.”

This month, Cain was accused of sexually harassing several women.

White said she decided to come forward because she feared that the affair would be uncovered after her name was passed on to reporters by someone who knew of the relationship.

“I’m not proud. I didn’t want to come out with this. I did not,” said White, who described the relationship with Cain as taking her away from her “humdrum life.”

“It was pretty simple. It wasn’t complicated. I was aware that he was married. I was also aware I was involved in a very inappropriate situation, relationship,” she said in the Fox interview.

The accusation comes as Cain continues to drop in national polls. Before the first sexual harassment allegations were published in Politico four weeks ago, some polls showed him leading the Republican race. Over the past month, it has been reported that four women accused Cain of sexual harassment while he headed the National Restaurant Association in the 1990s.

Cain has denied the allegations, although his campaign suffered as he and his aides bungled their response to the accusations. First, Cain refused to acknowledge that sexual harassment allegations had been filed against him. He later said he recalled one accusation but denied knowledge of the other and said they were all “baseless.”

Since then, he has fallen to 17 percent in CNN’s latest poll, compared with 20 percent for Mitt Romney and 24 percent for Newt Gingrich. Cain has been trying to refocus his campaign. He has a foreign policy address scheduled for Tuesday and a full day of campaigning set for Wednesday. But he seemed to expect the new accusation would further hurt his candidacy.

“I know that the court of public opinion is going to formulate its own opinion,” he told CNN. “I can’t control people who are going to make a decision based upon accusations.”

White did not respond to phone calls and e-mails Monday night. She said in the television interview that she met Cain in the late ’90s at a meeting in Louisville, when he was president of the restaurant association. They had drinks, she said, and he invited her to his hotel room, where he pulled out a calendar and suggested that she meet him in Palm Springs, Calif.

“He made it very intriguing,” White told the Fox affiliate.

White, who has worked as a fitness instructor, has been embroiled in conflicts that have led to court intervention. According to Georgia court records, she faced civil actions for nonpayment of rent. A former business partner, Kimberly Vay, sued White this year after a dispute that began when White wrote disparaging comments about Vay in a mass e-mail — comments that White recanted four months later as part of a legal settlement.

“She came back and stated that everything she stated in the e-mail was completely false,” Vay said in an interview. “She admitted to making it all up out of anger and frustration.”

The Fox affiliate described White as an unemployed, single mother of two.

The Cain campaign was alerted to the accusation by the television reporter, who had interviewed White over the weekend. White gave the reporter Cain’s private cellphone number — which appeared 61 times on her phone records over four months. When the reporter sent a text message to the number, Cain called back and said he knew White but had not had an affair with her.

On Monday, the candidate’s denial of the affair differed from a statement issued by his attorney, which said Cain has no obligation to answer questions about it.

“This is not an accusation of harassment in the workplace — this is not an accusation of an assault — which are subject matters of legitimate inquiry to a political candidate,” said Lin Wood, whom Cain hired after the sexual harassment allegations surfaced. “Rather, this appears to be an accusation of private, alleged consensual conduct between adults — a subject matter which is not a proper subject of inquiry by the media or the public. No individual, whether a private citizen, a candidate for public office or a public official, should be questioned about his or her private sexual life.”

Cain said repeatedly that there was no truth to White’s allegations of having stayed with him at the Ritz-Carlton in Atlanta’s Buckhead neighborhood or elsewhere. “We chased all of these other rumors for two weeks before, and as it turned out they were baseless . . . so we will address these when they come out. But at this point, I want to give you a heads-up. I don’t have anything to hide,” Cain said on CNN.

He said that he does not plan to drop out of the race but that his wife would have the final say.

Staff researcher Lucy Shackelford and polling analyst Scott Clement contributed to this report.