U.S. Republican presidential candidate Herman Cain has again denied allegations of sexual harassment and says they will not force him to drop his bid for his party's nomination.

During a news conference Tuesday in Scottsdale, Arizona, the presidential contender told reporters that chances of giving up his presidential bid “ain't gonna happen” and that “we will get through this.” Cain said he has never acted inappropriately with anyone and said the alleged incidents “simply did not happen.” Cain said he called his news conference because he wanted to speak directly to the American public.

Cain also said he would be willing to take a lie detector test if he had a good reason to do so.

Four women have accused Cain of sexual harassment. Two of them have spoken publicly about their accusations.

One of the women, Sharon Bialek, went before television cameras Monday as she accused him of inappropriate sexual behavior. Bialek says she was sexually harassed by Cain after seeking his help on an employment issue while he was head of the National Restaurant Association several years ago. She is the first person to publicly detail her claims.

During his news conference Tuesday, Cain said he does not know who Bialek is and does not recognize her name.

The second woman to speak publicly is Karen Kraushaar, who said she was one of two women who settled a claim against Cain with the restaurant association back in the 1990s.

Kraushaar is now a spokeswoman at the U.S. Treasury Department. Kraushaar tells The New York Times she was upset that her name was leaked in some media reports but decided to come forward now that her identity was known publicly. Kraushaar told the paper that “when you are being sexually harassed in the workplace, you are extremely vulnerable. Kraushaar also said, “You do whatever you can to quickly get yourself into a job some place safe, and that is what I thought I had achieved when I left.”

In a separate interview with The Washington Post newspaper, Kraushaar said she is interested in a joint press conference with the other women who have accused Cain of sexual harassment.

Cain has acknowledged he was the subject of such complaints but denied any wrongdoing.

Cain is a conservative African-American businessman whose only foray into politics ended in a failed bid for a U.S. Senate seat in Georgia. He has been at or near the top in recent national polls.