Updated

Herman Cain on Tuesday vigorously denied new claims of sexual harassment, calling a press conference in Arizona to declare the latest alleged incident "simply did not happen."

The Republican presidential candidate said he didn't even recognize the woman, Sharon Bialek, who a day earlier claimed he made unwanted sexual advances toward her 14 years ago.

"The charges and the accusations, I absolutely reject. They simply didn't happen. They simply did not happen," Cain said.

Cain, reading slowly and deliberately from notes for 10 minutes before taking questions from the media, said he has "never acted inappropriately with anyone -- period."

Declaring that he will stay in the 2012 race, Cain specifically addressed the charges leveled most recently by Bialek. Though Bialek said Cain sexually harassed her when she came to him about a job while he was heading the National Restaurant Association, Cain said that he was seeing her "for the very first time" when he watched her press conference on Monday.

"My first response in my mind and reaction was, I don't even know who this woman is," Cain said.

Cain's news conference came as another one of his accusers was revealed in media reports and subsequently came forward to speak about her allegations. Karen Kraushaar, who complained of sexual harassment by Cain while working at the National Restaurant Association, even says she now wants to hold a joint news conference with other Cain accusers.

"The reason sexual harassment is so difficult to prove is that workplace sexual predators try to make sure the victim is alone when the harassment takes place," Kraushaar said in a written statement issued after Cain's news conference. "The incidents in question occurred many years ago, but corroboration may still be possible with respect to some of the incidents, and in some cases it may even be possible to find witnesses."

The allegations have weighed on Cain's campaign for more than a week, as he has struggled to tamp down the controversy.

On Tuesday, Cain at first blamed the "Democrat machine" for bringing forward Bialek, a woman whom he described as "troubled" -- she has a history of financial problems, though she says she hasn't been offered money for coming forward. Pressed by Fox News to elaborate, Cain conceded he doesn't know who might be behind the allegations.

"We can only infer that someone is basically trying to wreck my character," Cain said.

The candidate at one point suggested he'd be open to taking a lie detector test, though he would need to have a "good reason" to do it.

Bialek, in an interview earlier with Fox News, said Cain absolutely knows who she is. She said she did not come forward until now because she was "embarrassed," and she only wants Cain to "admit to this."

"I know I'm speaking the truth, and that's what I want him to do is to say, 'Hey, you know, I've made some mistakes,'" she said on Fox News. Bialek said she presumed Cain will "deny it, unfortunately."

Cain said Tuesday that he's operating under the assumption that "there will probably be others," but only because the "machine" doesn't want a businessman in office.

Bialek was the fourth woman to claim Cain acted inappropriately toward her. Kraushaar, a spokeswoman for a Treasury Department office, was first identified by The Daily as one of the accusers. She later granted several interviews in which spoke of a "joint press conference" with the other women.

Cain acknowledged Kraushaar's case but said her claims were found to be "baseless."