While he described the accusations as "totally baseless and totally false", Cain did not directly refute the portion of the report that said the association paid out a financial settlement for at least two women, who ultimately left their jobs at the organisation.
"If the restaurant association did a settlement, I wasn't even aware of it, and I hope it wasn't for much because nothing happened," Cain told Fox.
But he did say: "Yes, I was falsely accused while I was at the National Restaurant Association." He said a subsequent investigation found no wrongdoing.
Cain, whose meteoric rise has put him neck and neck with Mitt Romney at the top of several opinion polls about the race for the Republican presidential nomination, insisted there were no other skeletons in his closet.
"The only other allegations would be trumped up allegations," he said. "There's nothing else."
The comments came just an hour before Cain was to address the National Press Club in Washington, where the audience was certain to ask about the scandal after he dodged an earlier direct question about the Politico report.
"I'll take all of the arrows later," Cain had said at the American Enterprise Institute, a Washington think-tank.
But when pressed by a reporter there, he said "I'm going by the ground rules that my hosts have set", referring to an AEI moderator's insistence that questions focus on fiscal policy and Cain's so-called "9-9-9" tax plan.
A spokesman for Cain had dismissed what he called a "thinly sourced allegation" against the candidate.
"This is something the establishment is trying to attack Mr Cain on," his spokesman JD Gordon said.
Cain, a businessman who is the former chief executive of the Godfather's Pizza chain, is also an ordained minister who has been married for some four decades.
At the AEI, Cain defended his signature tax plan, which proposes ditching the existing tax code and replacing it with a flat nine per cent personal tax, nine per cent business tax and nine per cent sales tax.
He said it was the best economic program laid out by Republicans challenging President Barack Obama, who has struggled to reduce the unemployment rate from a painfully high 9.1 per cent.
Cain acknowledged he was an "unconventional candidate" who would shake up American politics if he won the White House.
"Yes, I do have a sense of humour. Some people have a problem with that," he said as he left AEI. "Herman is going to stay Herman."
-AAP