WASHINGTON (AP) -- Denying he sexually harassed anyone, Republican presidential candidate Herman Cain said Monday he was falsely accused in the 1990s while he was head of the National Restaurant Association, and he branded revelation of the allegations a "witch hunt."

The former pizza company executive was responding to a Politico report that said the trade group gave financial settlements to at least two female employees who had accused Cain of inappropriate sexual behavior. He said he had no knowledge of whether the association provided any such settlements, and he declined to address specifics of the accusations or the resolution.

"There's nothing else there to dig up," he declared at the National Press Club. "We have no idea the source of this witch hunt, which is really what it is."

He added, "This bulls-eye on my back has gotten bigger."

Cain said an investigation into accusations of impropriety while he was the head of the restaurant group determined they were baseless.

"I've never sexually harassed anyone," he told Fox News.

Earlier in the day, Cain acknowledged, "I do have a sense of humor and some people have a problem with that." And by the afternoon, he was joking: "As a result of today's big news story, I really know what it feels like to be No. 1."

The trade association refused to comment on the allegations.

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

Cain - a self-styled outsider relatively new to the national spotlight - is facing a new level of scrutiny after a burst of momentum in the race for the GOP presidential nomination.

He's been at or near the top of national surveys and polls in early presidential nominating states, competitive with former Massachusetts Gov. Mitt Romney, long considered the Republican to beat. Cain has been pointing to his long record in business to argue that he has the credentials to be president during a time of economic strife.

So far, Cain has seemed to weather a series of stumbles; the former radio talk show host had to clarify recent statements on abortion, the treatment of terrorism suspects and the placing of an electrified fence along the U.S.-Mexico border. He's also shrugged off questions that have started to surface about his management style, including criticisms about a lackluster approach to his own presidential campaign. He lags his top competitors in organization and fundraising.

The new allegations could hurt Cain's efforts to reassure the Republican establishment that someone with so little political experience - and who hasn't been fully vetted on a national stage - is prepared to go up against President Barack Obama next fall.

But there were signs that conservatives were rallying behind him, attacking the report as inaccurate and perhaps racially motivated.

The head of the conservative Media Research Center, Brent Bozell, called the Politico story a "High-tech lynching of Herman Cain." That was a reference to Supreme Court Justice Clarence Thomas' response to a former worker's allegations during his confirmation hearing.

"In the eyes of the liberal media, Herman Cain is just another uppity black American who has had the audacity to leave the liberal plantation," Bozell wrote on the conservative website Newsbusters.org.

The allegations came to light Sunday night when Politico reported that at least two women who complained about sexually inappropriate behavior while working for Cain had signed agreements with the restaurant group that gave them five-figure financial payouts to leave the association and barred them from discussing their departures. Neither woman was identified.

The report was based on anonymous sources and, in one case, what the publication said was a review of documentation that described the allegations and the resolution. Politico said spokesman J.D. Gordon told their publication that Cain himself had indicated to campaign officials that he was "vaguely familiar" with the charges and that the restaurant association's general counsel had resolved the matter.

But Cain, himself, refused to comment to Politico when asked specifically about one of the woman's claims. And when asked if he had ever been accused of harassment by a woman, the publication said Cain responded by asking the reporter, "Have you ever been accused of sexual harassment?"

In a statement late Sunday to The Associated Press, Gordon told the AP that the Politico report was not true - and blamed the media.

"Inside-the-Beltway media have begun to launch unsubstantiated personal attacks on Cain," Gordon said in a written statement. "Dredging up thinly sourced allegations stemming from Mr. Cain's tenure as the chief executive officer at the National Restaurant Association in the 1990s, political trade press are now casting aspersions on his character and spreading rumors that never stood up to the facts."

Despite the controversy, Cain pressed ahead with his full slate of campaign appearances in Washington on Monday.

At a speech at the American Enterprise Institute, he refused to answer questions about the allegations but said he would further discuss them later in the day while appearing at the National Press Club.

Still, as he was leaving the stage, he stopped, turned to the crowd and talked about his sense of humor without providing any context. He said his staff tells him to be himself - or "Let Herman be Herman."

He added: "Herman is going to stay Herman."

An hour later, he was on Fox News.

"If more allegations come, I assure you, people will simply make them up," Cain said. Besides his job as CEO of Godfather's Pizza, he worked at the Federal Reserve Bank of Kansas City.

"What you can expect from my campaign is for me to stay on message, for us to continue to do the things and execute our strategy in order to win the nomination," Cain said.

Still, he acknowledged that the controversy could become a significant political problem.

"Obviously, some people are going to be turned off by this cloud that someone wanted to put over my campaign," he said. "But a lot of people aren't going to be turned off. We'll just have to wait and see what happens."

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