Herman Cain, one of a crowded field seeking the Republican nomination for next year's U.S. presidential election, says he won't withdraw from the race despite a slew of women coming forward with sexual harassment allegations.

At a press conference called specifically to address the allegations from four separate women, Cain said Tuesday it "ain't gonna happen" when asked if he would shelve his campaign.

Cain said that while sexual harassment allegations are serious, the accusations being levelled against him are "false."

"I will vigorously defend my reputation, because I will not allow false accusations to compromise or in any way shed badly on my character or my integrity," Cain said firmly.

He went on to say that he has "never acted inappropriately with anyone, period."

Cain's press conference came a day after the most recent woman to come forward with allegations, Sharon Bialek, told reporters in graphic detail about an incident she says happened in 1997.

Bialek alleged that Cain reached under her skirt and pulled her head toward his crotch while in Washington to seek help finding a job.

Bialek had worked at the educational foundation of the National Restaurant Association from 1996 to 1997 before being fired. Cain was head of the organization at the time.

Bialek said she did not file a complaint with the association at the time because she was no longer employed by the organization.

On Tuesday, Cain called Bialek a "troubled woman" who was brought forward by the "Democratic machine" to smear his reputation. Cain said he had never seen Bialek before her press conference, and that "these accusations that were revealed yesterday simply did not happen."

When asked by a reporter if he would take a lie-detector test, Cain said he "absolutely would," but only if he had good reason to.

Shortly before Cain spoke to reporters, one of his accusers told U.S. media outlets that she hoped to hold a joint press conference with the other women so "all of these allegations could be reviewed as a collective body of evidence."

Karen Kraushaar, 55, a senior spokesperson at the U.S. Treasury Department, first accused Cain of sexual harassment back in the 1990s. She had originally wished to remain anonymous until her name was made public on Tuesday.

"When you're in a work situation where you are being sexually harassed, you are in an extremely vulnerable position," Kraushaar told The Washington Post. "You do whatever you can to quickly get yourself a job someplace where you will be safe. That is what I thought I had achieved when I left."

Of Kraushaar's accusations, Cain said an investigation found them to be "baseless." He said the only incident involving Kraushaar that he could recall was when he indicated with a hand to his chin that she was as tall as his wife.

When asked why four women were coming forward now with allegations of harassment, Cain said running for office means various accusations "come out of the woodwork."

He said that while he does not have any direct evidence of a conspiracy to keep him out of the White House, he feels "someone is deliberately behind this."

"I happen to think where it's coming from is that some people don't want to see Herman Cain get the Republican nomination," he said.

"And some don't want to see Herman Cain become the president of the United States of America."