During a press conference on Tuesday afternoon, Republican presidential candidate Herman Cain denied all allegations of sexual harassment leveled against him.

"I have never acted inappropriately with anyone, period," he insisted. "The charges and the accusations I absolutely reject. They simply didn't happen. They simply did not happen."

Cain also said the allegations would not force him to abandon his campaign for president.

"As far as these accusations causing me to back off and maybe withdraw from this primary race, ain't gonna happen, because I am doing this for the American people and for the children and the grandchildren."

Sharon Bialek, who is a registered Republican and tea party supporter, told reporters Monday that the then-CEO of the National Restaurant Association (NRA) had put his hand “under my skirt and reached for my genitals” while she was meeting with him about a job in mid-July 1997.

Cain claimed the first time he saw Bialek was during her press conference.

"As they got to the microphone, my first thought was, 'I don't even know who this woman is,' " he said.

Three other women have also accused him of engaging in aggressive and unwanted behavior.

“The fact is, these anonymous allegations are false, and now the Democrat machine in America has brought forth a troubled woman to make false accusations, many of which exceed common sense, and they certainly exceed the standards of decency in America."

Politico reported last week that when Cain was head of the National Restaurant Association, a post he held from 1996 to 1999, two females employees had complained about his inappropriate behavior, including conversations allegedly filled with innuendo and sexually suggestive questions.

The women left the group after signing agreements that provided them with financial payouts but prohibited them from talking about the reasons for their departure.

News reports on Tuesday identified one of the women as Karen Kraushaar.

A third woman later told the Associated Press that she had considered filing a complaint against Cain around the same time the two co-other women had settled separate harassment complaints against him.

The allegations sparked a media frenzy that has engulf his campaign.

Cain acknowledged that allegations of sexual harassment were made against him, but denied being guilty. He claimed the allegations were "found to be baseless."

"I happen to think where it's coming from is that some people don't want to see Herman Cain to get the Republican nomination, and some people don't want Herman Cain to become the president of the United States of America," Cain said.