Herman Cain has scheduled a Tuesday afternoon press conference to take "head on" multiple allegations of sexual harassment after appearing on a late-night comedy show to declare as a fabrication accusations from a fourth woman claiming sexual harassment.

"There is not an ounce of truth in all of these accusations," Cain told talk show host Jimmy Kimmel, saying the latest claims made him angry and he wants to "set the record straight." 

Ahead of Cain's scheduled press conference in Phoenix, the woman who first went public Monday to allege Cain had tried to manhandle her in 1997 said she hopes the Republican presidential candidate admits to being "inappropriate" with women. 

Sharon Bialek, who described an alleged incident in a car after the two dined together to discuss his help in her getting a job,  told Fox News on Tuesday that she did not come forward until now because she was "embarrassed," and she only wants Cain to "admit to this." 

"I want him to acknowledge that at points in time in his life, he's been inappropriate with women. I don't know what the other allegations are. I know what mine are. 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 presumes Cain will "deny it, unfortunately." 

One of the earlier accusers was also identified Tuesday by The Daily as Karen Kraushaar. The article said Kraushaar, a Maryland resident being represented by attorney Joel Bennett, currently works as the communications director for the Treasury Department's inspector general's office. Though she works under the Obama administration now, she also was employed as a communications analyst for an IRS agency under the Bush administration. 

Bennett, asked about the report, told Fox News he "cannot deny that is her name." But he said his client "prefers to remain private and not become a public figure." 

Cain unequivocally denied the harassment claims in the interview Monday night. He described to Kimmel watching the Bialek press conference on Monday, which he said his wife, Gloria, also watched while home in Atlanta. 

"And as I was sitting there I had a few of my staff members there with me, and I'm sitting here and they're watching me, and they can see steam coming from my ears and the feelings that you have when you know all of this is totally fabricated you go from anger ... then you get disgusted," Cain said. 

Bialek said she felt the same way.

"Yesterday when I went into this, I was completely fine. As this day has progressed, I'm feeling all those feelings that Herman's feeling, the anger, the frustration. Only, I know the truth, and he's not telling it," she said.

The decision to hold a press conference is a reversal from just days ago when Cain told reporters he was done answering questions about at least three anonymous sexual harassment allegations. But he told Kimmel that now that the accuser has a name, he wants to respond again.

Despite the developments, Cain backers remained solidly behind the former pizza company executive. They pointed to the presence of Gloria Allred -- a high-profile attorney with Democratic ties -- alongside Bialek at a news conference on Monday in New York as proof that the latest claim was a partisan smear. 

"The fact that she's involved removes all credibility," Georgia Christian Coalition president Jerry Luquire said. "If he says he didn't do anything than I believe him." 

Bialek is the fourth woman to say that Cain engaged in inappropriate behavior during his time at the helm of the restaurant group. At least two women who worked there at the time filed sexual harassment complaints. 

A third woman told The Associated Press last week that she considered filing a workplace complaint against Cain over what she deemed sexually suggestive remarks and gestures that included a private invitation to his corporate apartment. And a former pollster for the restaurant association has said he witnessed yet another episode involving a different woman. 

Trying to stay on-message, the Cain campaign released a new web video -- targeting voters in the lead-off caucus state of Iowa -- highlighting what it says are excessive federal regulations on farmers that are driving up costs for consumers. 

But aides made clear that Cain will fight the allegations, casting them as baseless. 

"The questions the media should be asking are who's paying for Gloria Allred's fee, how did Ms. Bialek get introduced to Ms. Allred, and was she paid to come forward with these false accusations or was she promised employment?" the news release said. 

Bialek said that she hasn't given any thought to writing a book about the incident or making money elsewhere, but "this isn't why I came forward." She also acknowledged that she lives in the same building in Chicago as President Obama's top adviser, David Axelrod, but has never spoken to him and is a registered Republican.

The Associated Press contributed to this report.