Republican Herman Cain directly confronted allegations on Tuesday that he had sexually harassed women, saying his latest accuser had lied and promising to continue his quest for the presidency.

Addressing the controversy before a throng of reporters in suburban Phoenix, Cain said he had no recollection of ever meeting Sharon Bialek, the woman who went public Monday and accused him of groping her in a car after the two dined together in Washington 14 years ago. He called her account “baseless, bogus and false” and said Bialek and three other women who have accused him of sexual harassment are part of a coordinated effort to attack his character and derail his campaign.

“We are not going to allow Washington or politics to deny me the opportunity to represent this great nation,” Cain said, adding that he was willing to take a lie-detector test. “As far as these accusations causing me to back off and maybe withdraw from this presidential primary race — ain’t gonna happen.”

The controversy over the charges escalated just minutes before Cain’s news conference, when one of the previously anonymous women accusing him of inappropriate behavior decided to reveal her name after it appeared on news sites. She urged the other accusers to hold a news conference with her.

Karen Kraushaar, 55, a communications official for the Treasury Department’s inspector general for tax administration, filed a claim of sexual harassment against Cain when he headed the National Restaurant Association and she was an employee there in the 1990s. She received a payment when she left the organization, but Cain, who disputed the allegations at the time, was not a party to the agreement.

“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 wrote in an e-mail after Cain’s news conference.

“Though reliving the matter is extremely painful, it is now no longer a private matter but a matter of public interest,” she said, adding that if her employer allows, she will appear with other women who have accused Cain “so that we can present together what happened.”

After more than a week of news stories about the allegations, Cain decided to address the public directly after Bialek delivered her detailed accusations Monday.

At her news conference, Bialek, a 50-year-old single mother who worked briefly in the restaurant association’s Chicago office, said Cain was driving her back to her hotel after their dinner when he pulled the car over, pushed his hand up her skirt and pushed her head down toward his crotch. She said she had asked to meet with him, at the urging of her then-boyfriend, to seek Cain’s help in finding work after losing her job at the association.

It was the first time one of Cain’s accusers had allowed her name to be used or appeared in public. And the graphic nature of the allegations removed the possibility that Cain’s accusers could have misunderstood his sense of humor, as some of his supporters suggested.

The account prompted strong reaction from a number of prominent politicians, including some of Cain’s rivals for the Republican presidential nomination.

In an interview with ABC News on Tuesday, former Massachusetts governor Mitt Romney called the allegations “disturbing” and said that “they’re going to have to be addressed seriously.”

Former House speaker Newt Gingrich, in a separate interview with ABC, said: “Clearly Herman Cain has to answer the charges, he has to do so in a way that’s convincing, and I think that’s unavoidable. He owes her that, and he also owes the American people that.”

Gingrich added: “And it has to be accurate, because if it’s not accurate, it won’t last 24 hours.”

Polls continue to show Cain at the top of the field in the GOP presidential contest, effectively tied for first place with Romney. Cain campaign officials said no supporters have told them that they are withdrawing their backing. And many supporters professed their continued support for the candidate.

“We don’t elect a president on rumor and innuendo and allegation,” said Thad Altman, a Florida state senator and a co-chairman of Cain’s campaign there. “It’s so easy for people to step forward and say things. I think the truth will come out in the long term. I’m not concerned in any way shape or form.”

At his news conference, Cain refused to utter Bialek’s name. The former Godfather’s Pizza executive said, “I don’t even know who this lady is,” and he described her as a “troubled woman” — an apparent reference to her financial difficulties, which include two bankruptcies and a federal tax lien.

Cain and his supporters have sharply questioned Bialek’s motives and version of events. A Cain spokesman cast her as a “woman with a long history of severe financial difficulties, including personal bankruptcy,” and asked, “Was she paid to come forward with these false accusations, or was she promised employment?”

In her interviews, Bialek denied that she is benefiting financially from her accusations and said she came forward in part because other women Cain allegedly sexually harassed have remained silent.

“I was not paid to come forward, nor was I promised any employment,” she told ABC News. “I was embarrassed, as many women are in these kinds of situations, and I kind of just wanted it to go away.”

Regarding Kraushaar’s accusations, Cain said that they were “found to be baseless.”

Cain appeared at the news conference alongside his lawyer, Atlanta-based L. Lin Wood, who has represented Richard Jewell and Rep. Gary Condit (D-Calif.), both falsely accused of wrongdoing.

In one of the more emotional moments of Cain’s appearance, he recounted calling his wife, Gloria, after watching Bialek’s TV appearance Monday afternoon.

“Hi, Sweetheart, did you see it?” Cain recalled asking.

“Yes,” he said she replied.

“What did you think?”

“I have known you for 46 years,” Cain said his wife told him. “That doesn’t even sound like anything you would ever do to anyone.”

Cain said he is under attack because those who benefit from the status quo in Washington do not want a businessman in the White House: “They really don’t want to see an unconventional candidate that is connecting with the people and putting bold solutions on the table.”

He added: “Sexual harassment is a very serious charge. Throughout my career, I have had nothing but the utmost respect for any and all women, as well as those that have worked under my leadership.”

Staff writers Aaron Davis, James V. Grimaldi, Nia-Malika Henderson and Krissah Thompson; staff researcher Lucy Shackelford; and research editor Alice Crites contributed to this report.