A new woman has come forward with allegations against Republican presidential candidate Herman Cain, this time claiming the two had a 13-year extramarital affair, but Cain and his advisers deny the claims, just as they have denied the sexual harassment claims that have set back his campaign.

Cain, in an apparent effort to get ahead of the story, appeared Monday afternoon in a cable news interview before the Georgia woman's story aired and said she is "someone who I know, who is an acquaintance, who I thought was a friend," though he denied an affair.

He later issued a statement suggesting the woman's story was another example of "dirty politics and smear tactics" and evidence some people are "afraid of a Cain presidency."

"My plan is to continue to spread my vision on how I would renew America and keep her safe," he said. "I will not fight false claims, as it is not what America needs or wants."

The woman, an Atlanta businesswoman named Ginger White, made the claims in an interview with the Fox affiliate in Atlanta that aired later Monday, details of which were released on the station's website, MyFoxAtlanta.com, after Cain came forward.

"It was pretty simple," White told the station. "It wasn't complicated. I was aware that he was married. And I was also aware that I was involved in a very inappropriate situation, relationship."

She said they met in the late 1990s when Cain, as president of the National Restaurant Association, was making a presentation in Louisville, Ky. He later would fly her to cities where he was speaking and give her gifts, she told the TV station.

"He made it very intriguing. It was fun," White said. "It was something that took me away from my sort of humdrum life at the time, and it was exciting."

Cain never harassed her or treated her poorly, though their physical relationship ended eight months ago, just before Cain announced his candidacy for president, White said. She provided some text messages and phone bills as documentation of her contact with Cain, including as recently as September.

The station also released a statement from Cain's attorney, Lin Wood, who said the allegations of "private, alleged consensual conduct between adults" is not "not a proper subject of inquiry by the media or the public."

A campaign official who asked to remain anonymous also denied White's claims, telling Fox News they are "baseless false accusations."

The new allegations are only the latest setback for Cain, who has seen his popularity fade since reports surfaced one month ago of sexual harassment allegations dating back to his tenure with the National Restaurant Association.

Although the latest report involves an alleged consensual relationship, the claims may further weaken his support among conservative Republicans concerned about social issues, including the institution of marriage.

Cain has been married for 43 years. His wife, Gloria, rarely appears on the campaign trail but agreed to her first televised interview after the sexual harassment allegations broke.

"I seriously, in my soul, don't think he's that type of person," she said of the charges during the interview on Fox News' "On The Record with Greta Van Susteren."

She acknowledged, however, that their marriage was not perfect.

"There have been troubles ... [but] we have loved each other for 43 years," she said.

Newscore contributed to this report.