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Amid his repeated denials that he harassed women at the National Restaurant Association in the late 1990s, Republican presidential candidate Herman Cain entertained the notion that the fire surrounding him might have been ignited by his rivals.

“This bull’s-eye on my back has gotten bigger,” the former businessman said at a luncheon at the National Press Club this afternoon. “We have no idea of the source of this witch hunt, which is what it is.”

Cain acknowledged twice today that sexual harassment charges were brought against him, but dismissed them as false and baseless.

“In all my over 40 years of business experience … I have never sexually harassed anyone,” Cain said. “While at the Restaurant Association, I was accused of sexual harassment – falsely accused, I might add.”

Cain said he allowed the association’s general counsel and human resources manager to look into the allegations, and that the investigation found no basis for the charges. But the head of the human resources department at the time, Mary Ose, told Politico that she was not aware of any complaints against Cain during that time.

The former chief executive of Godfather’s Pizza also said he was unaware of any reported settlement that gave the women money to leave the National Restaurant Association and not talk about the charges.

“If the Restaurant Association did a settlement, I wasn’t aware of it and I hope it wasn’t much because nothing happened,” Cain said in a Fox News interview this morning.

The National Restaurant Association would not comment on the allegations or whether a settlement was made.

“The incidents in question relate to personnel matters that allegedly took place nearly fifteen years ago,” spokeswoman Sue Hensley said in a statement today. “Consistent with our longstanding policy, we don’t comment on personnel issues relating to current or former employees.”

In an interview with Fox News’ Greta Van Susteren, to air tonight, Cain said he remembered only one woman filing a formal complaint, the Washington Examiner reports. When asked what might have led to that accusation, Cain said he once made a gesture — with his palm near his chin — telling the woman she was the same height as his wife. That incident, Cain said, was included in a complaint as having made the woman uncomfortable.

Cain had, until today, dodged questions about the allegations, which were first reported by Politico. When confronted on the trail Sunday, the GOP candidate refused to comment, instead asking the reporter whether he had ever been accused of sexual harassment.

At an event this morning to discuss his tax plan, Cain told the audience, ”I do have a sense of humor and some people have a problem with that.”

“Herman be Herman, and Herman is going to stay Herman,” he said before exiting the room.

Cain’s chief of staff, Mark Block, appeared on MSNBC this morning to defend Cain, and questioned the Politico report.

“Every negative word and accusation in the article is sourced to a series of unnamed or anonymous sources. Questionable at best,” Block said of the Politico story, which found that Cain was accused of inappropriate behavior by two women during his tenure as National Restaurant Association head from 1996 to 1999.

Per Politico, “the women complained of sexually suggestive behavior by Cain that made them angry and uncomfortable, the sources said, and they signed agreements with the restaurant group that gave them financial payouts to leave the association. The agreements also included language that bars the women from talking about their departures.”

Block said he is not aware of any cash settlement, and when he asked his boss of the allegations, Cain said, “bring me some facts. Bring me the accuser.”

Throughout his appearance in Washington this morning, Cain appeared to be in relatively good spirits. He opened his remarks at the American Enterprise Institute with a joke – prompted by the moderator – that he’d like to dress up as GOP rival Ron Paul for Halloween.

At the National Press Club, he joked about making it into the headlines this weekend.

“As a result of today’s big news story, I really know what it feels like to be number one,” he quipped.

He then ended the speech with a gospel song, “ He Looked Beyond My Faults.”

But the sexual harassment allegations could be damaging for the candidate who has surged to the top of the polls despite, as he acknowledged himself, an “unconventional campaign.”

According to Politico, the conversations between Cain and the two women who accused him of inappropriate behavior were “filled with innuendo or personal questions of a sexually suggestive nature, taking place at hotels during conferences, at other officially sanctioned restaurant association events and at the association’s offices.

“There were also descriptions of physical gestures that were not overtly sexual but that made women who experienced or witnessed them uncomfortable and that they regarded as improper in a professional relationship,” the article stated.

ABC News’ Susan Archer, Devin Dwyer and Michael Falcone contributed to this report.