U.S. Republican presidential hopeful Herman Cain appeared on "Late Show with David Letterman" and denied allegations of sexual harassment.

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Letterman joked with the politician about his own sex scandal during the taping of Friday night's show.

A CBS producer was sentenced to six months in jail for attempting to blackmail Letterman in 2009 in exchange for his silence regarding the married comedian's sexual relationships with staffers.

During Cain's visit to "Late Show," Letterman asked the politician about the allegations that have plagued his campaign.

"Now we go to the National Restaurant Association. Isn't that the origin of the sexual-harassment charges?"

"That's the origin of the accusations which were found to be baseless," Cain replied. "Now, remember this: In my entire career, no accusations were ever made of that sort, not until I got inside the Beltway in Washington, D.C."

"Right, well, that's the way it works," Letterman said. "You put something under a microscope; we're going to find amoebas."

"Yes," Cain said.

"But one of two things will happen with the sexual harassment, and I'm no stranger to sexual scandal. ... One of two things will happen," Letterman said. "You will be proven -- you'll be exonerated… You'll be like Justin Bieber, all of that's going away. Or, they will prevail and there will be somebody else going forward, 'Herman did this, this is the money I received and here's exactly the documentation you need to prove that he's lying.' Now what happens if that's the case? Will you drop out of the campaign if that's the case?"

"Well, first of all, let's be very clear about the accusations that have already been made," Cain said. "The reason that I went front and center in front of the media is because I knew that there wasn't anything to it. There's no borne documentation… nothing else has come up, so we have moved on."

"So, these statements are all false," Letterman said. "All of these women are lying."

"Did not happen," Cain said.

"They are all lying," Letterman said.

"Yes, they are," Cain said.