Updated: 7:09 p.m. ET
Ginger White, an Atlanta-based woman, is coming forward with allegations that she had a 13-year-long extramarital affair with Herman Cain.
In an interview with Atlanta's FOX 5 News which aired Monday night, White told FOX 5's Dale Russell that she had an ongoing affair with Cain starting in the late 1990s, when Cain was president of the National Restaurant Association, until about eight months ago - right before he started running for president, according to a report from the Fox affiliate.
"I'm not proud," White said. "I didn't want to come out with this. I did not."
"It was pretty simple," she added. "It wasn't complicated. I was aware that he was married. And I was also aware I was involved in a very inappropriate situation, relationship."
In anbefore White's interview aired, Cain said he knew the woman but denied that they had had an affair.
As CBS News political correspondent Jan Crawford reports, a statement provided to CBS News from Cain attorney Lin Wood did not go so far as to deny an affair. Wood's statement said White's accusations of a consensual affair between two adults was not a legitimate news story.
"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," Wood said in the statement. "He 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."
According to FOX 5, White showed reporters from the network cell phone bills that showed 61 calls or text messages - including in the early-morning and evening hours - from what she said was Cain's private cell phone number.
FOX 5 says its reporters texted that phone number and received a call back from Cain. "He told us he 'knew Ginger White' but said these are 'more false allegations.' He said she had his number because he was 'trying to help her financially,'" the report states.
White appears to have struggled financially in the past: According to FOX 5, she filed bankruptcy in Kentucky more than 20 years ago, and has been served with a number of eviction notices, including one within the last month. She also filed a sexual harassment claim against an employer in 2001, the case for which has since been settled, FOX 5 reports.
In the interview, White emphasized that Cain never harassed her and that he treated her well throughout the duration of their affair.
"He made it very intriguing," White said. "It was fun. It was something that took me away from my humdrum life at the time. And it was exciting."
When questioned about whether or not her relationship with Cain was ongoing currently, White said "I think it is safe to say that after this interview, that will be the end of it. Yes, we have a friendship now."
In a statement released after White's interview aired, Cain said he would "not fight false claims as it is not what America needs or wants."
"The American public is tired of dirty politics and smear tactics as evident of their tremendous outpouring of support for me, my family and my campaign this past month," he said. "I am running for President of the United States of America and the reality is that there are individuals out there that favor the status quo of higher taxes, more government and political cronyism and they are afraid of a Cain Presidency."
Cain added: "I have spoken directly to the American people and have been 100 percent honest with them. My plan is to continue to spread my vision on how I would renew America and keep her safe. I will not fight false claims as it is not what America needs or wants," continued Mr. Cain.
Two women, Karen Kraushaar and Sharon Bialek, have come forward to publicly accuse Cain of sexual misconduct in the 1990s, while he was head of the National Restaurant Association. Bialek has accused Cain of putting his hand under her skirt and pushing her head toward his crotch after a dinner meeting in 1997. Two women have also made anonymous accusations against Cain for sexual misconduct.
Cain has repeatedly denied the allegations, saying, "I have never acted inappropriately with anyone. Period." Speaking of Bialek, he suggested that "the Democrat machine" brought forth "a troubled woman" in an effort to bring him down.Full CBS News coverage: Herman Cain