She was the fourth woman to make allegations against Cain; the other three have remained anonymous.
"I want you, Mr. Cain, to come clean," Sharon Bialek of Chicago said. "I want you to admit you were inappropriate to people."
CNN read a statement from the Cain campaign that called the accusations by the four women "bogus attacks."
"All allegations are completely false," the statement said.
Supporters of Cain, a former pizza industry executive who was president of the National Restaurant Association in the 1990s, had challenged the credibility of the first three women, saying their anonymity made it difficult for Cain to respond directly to the allegations.
Bialek told of a 1997 incident she said occurred when she met with Cain in Washington after she was fired from her post with the association's national education foundation. Bialek said the alleged incident occurred while the two were in a car near the association's headquarters.
"Instead of going into the offices, he suddenly reached over and put his hand on my leg, up my skirt, and reached for my genitals," Bialek said. She said he pushed her head "toward his crotch."
Bialek said she was shocked and when she protested the advances Cain responded, "You want a job right?"
She told him to stop and take her to her hotel, which he did, Bialek said.
She said she told her boyfriend -- who had suggested she contact Cain for help in her job search -- and another friend about the incident. Her attorney, Gloria Allred, displayed sworn statements from the two. Bialek said she didn't tell the association because she wasn't working for the trade group at the time.
Bialek said she didn't want to be at the news conference in New York, and wouldn't have been if three other women hadn't said anonymously they were subjected to inappropriate behavior by Cain.
"I implore you, Mr. Cain, [to] make this right so that you and the country can move forward …," Bialek said.
When introducing Bialek, Allred said her client was "brave to come forward. … She will face public scrutiny. We applaud her for her courage."
If the allegations by the women are true, "then I, for one, am disgusted by Mr. Cain's serial sexual harassment" toward women, Allred said.
Before the news conference, the Cain campaign took its case to Twitter, directing visitors to the candidate's Iowa caucus fundraiser, The Hill reported.
"Welcome to the campaign, Gloria Allred. What took you so long?" a Twitter account associated with the Cain campaign said.
The Twitter ID hadn't been verified by the social networking site but has been repeatedly re-posted by Cain's official Twitter page.
Allred's clientele include women involved sexual harassment cases with former Rep. Anthony Weiner, D-N.Y., golfer Tiger Woods and HP Chief Executive Officer Mark Hurd. She also worked with Nicole Brown Simpson's family during the O.J. Simpson murder trial.