Updated, 6:59 p.m. ET: Ginger White made her allegations public in a Monday night interview. Read more
Herman Cain revealed Monday that an Atlanta-area woman is coming forward alleging an "extended" 13-year extramarital affair with the Republican presidential candidate.
Cain told CNN the woman's claims are untrue.
The former Godfather's Pizza CEO told CNN's Wolf Blitzer he wanted to "give you a heads up and everyone a heads up" that the woman would be coming forward.
He said he knows the woman, but denied having had an affair with her.
"I did not have an affair," he said. "I have done nothing wrong."
According to an Atlanta affiliate of Fox News, the woman, who has been identified as Ginger White, is claiming she and Cain were romantically involved for 13 years.
"It was pretty simple," White told the Fox affiliate, which aired its report at 6:00 p.m. Eastern Time. "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."
Watch the report at the bottom of this post
Cain described the woman as an "acquaintance who I thought was a friend" and said his campaign was going to handle the charges "detail by detail, accusation by accusation."
When asked explicitly if he had either sex or an affair with the woman, Cain said "no."
He declined to respond more specifically without more detailed knowledge of what the woman was alleging.
"This individual's going to accuse me of an affair for an extended period of time. I don't want to specify because I don't know what's in the story," Cain said. "Through my attorney, we will respond to every detail and every allegation."
In a statement to the Fox affiliate, Cain attorney Lin Wood argued that the accusations were regarding "a subject matter which is not a proper subject of inquiry by the media or the public" and said Cain had no "obligation" to discuss them publicly.
"Mr. Cain has alerted his wife to this new accusation and discussed it with her. 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," Wood said.
"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 added in the statement.
Cain told Blitzer he did not plan to drop out of the race in light of the allegations, but said he was concerned for the impact they might have on his family.
"If I drop out because of this kind of mess, then the system wins and
one of the reasons I'm running is to change the system," Cain said. "I'm more worried this is going to hurt my family, not my campaign."
Still, he said, "As long as my wife believes that I should stay in this race, I'm staying in this race."
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.
The allegations, which first broke at the end of October, appear to have hurt Cain in opinion polls. From the middle of October through the first week of November, Cain was polling in the 20-30 percent range, putting him atop polls of the GOP presidential contenders. Recent polls show him sliding to support in the mid-teens, behind Mitt Romney and Newt Gingrich.
Read Cain attorney Lin Wood's full statement below:
"Mr. Cain has been informed today that your television station plans to broadcast a story this evening in which a female will make an accusation that she engaged in a 13-year long physical relationship with Mr. Cain. 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.
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. The public's right to know and the media's right to report has boundaries and most certainly those boundaries end outside of one's bedroom door.
Mr. Cain has alerted his wife to this new accusation and discussed it with her. 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."Full CBS News coverage: Herman Cain