WASHINGTON — A Georgia businesswoman said Monday she and Herman Cain had a 13-year extramarital affair, an allegation the Republican presidential hopeful denied as strongly as earlier allegations of sexual harassment.

“Here we go again. I didn’t do anything wrong,” Cain said on CNN. He acknowledged he knew the woman who was behind the accusation.

Moments after Cain issued a preemptive denial, an Atlanta television station posted a story to its website quoting a woman identified as Ginger White as saying, “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.”

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 surveys, and more recently eclipsed by Newt Gingrich in the race to emerge as the principle conservative alternative to Mitt Romney.

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.”

Asked if he suspected his accuser had emails, letters, gifts or other possible evidence of an affair, he said, “No.”