The lawyer, Joel Bennett, said his client - married then and now - accepted a financial settlement in leaving her job at the National Restaurant Association shortly after lodging the complaint against Cain, who was then the trade group's head. Bennett did not name the woman, who he said had decided not "to relive the specifics" of the incidents in a public forum.
Cain, who tried to return to normal campaigning Friday, has repeatedly denied ever sexually harassing anyone. His spokesman, J.D. Gordon, said in response to Bennett's comments, ""We're looking to put this issue behind us and focus on the real issues, which are fixing this broken economy, putting Americans back to work and strengthening national security."
Apart from disclosing that his client alleged more than one incident, Bennett's remarks added little of substance to a controversy that erupted nearly a week ago.
"She made a complaint in good faith about a series of inappropriate behaviors and unwanted advances from the CEO" of the restaurant organization, he said.
In a statement late in the day, Dawn Sweeney, the trade group's current CEO, said Cain had disputed the allegations at the time they were made. Cain has contended an internal investigation at the time of the complaint showed no evidence of improper conduct by him, but Sweeney did not address that issue.
Bennett's comments to reporters outside his law office came as Cain was making a concerted effort to show he would no longer allow the controversy to dominate his unlikely challenge for the GOP presidential nomination.
The candidate drew cheers of support Friday from conservative activists as he delivered a speech focused on the U.S. economy. He is trying to convert his meteoric rise in opinion polls into a campaign organization robust enough to compete with Mitt Romney, Rick Perry and other rivals in early primary and caucus states.
In an appearance before the Americans For Prosperity Foundation, the career businessman pitched his trademark 9-9-9 economic program and referred only elliptically to the controversy that has overshadowed his campaign in recent days. "I've been in Washington all week, and I've attracted a little bit of attention," he said to knowing laughter from his audience.
Not everyone sounded ready to let it fade.
In Georgia, the state party chairwoman, Sue Everhart, said, "I think he has to completely put it behind him or it will continue to be a problem. He's got to do the housekeeping duties and clean this up."
She suggested Cain should coax the restaurant trade group to permit one of his accusers to make a public statement. That was before the woman's lawyer read her statement, with the trade group's permission.
The woman, whose identity has not been made public, signed a confidentiality agreement when she left the organization more than a decade ago after accusing Cain, then the trade group's head, of sexual harassment. At the time of her departure, she received a financial settlement. The lawyer declined to say how much it had been.
At least two other women have made similar allegations, and a former pollster for the restaurant association has said he witnessed yet another episode.
The controversy surfaced as Cain, a black man in a party that draws its support overwhelmingly from white voters, was rising to the top in public opinion polls. His campaign announced Friday that donations so far this week have totaled $1.6 million, described as a fourfold increase over the average take for an entire month.
Official figures won't be available for weeks, but to judge from Cain's existing campaign organization, it could hardly come at a better time for him.
In Iowa, where caucuses kick off the campaign year on Jan. 3, Cain has a modest presence at best.
He let more than two months lapse between visits on Aug. 13 and Oct. 22, and aides say they don't expect him to return to the state until Nov. 19.
He employs four full-time staff in the state, while Perry and Rep. Michel Bachmann of Minnesota each have 10 on their campaign payroll. Romney, who is still evaluating how strenuously to compete in the state, also has a bigger staff than Cain.
Cain also trails his rivals in the endorsement competition in Iowa, an important but hardly foolproof indication of a candidate's viability.
Lisa Lockwood, a spokesman for Cain's campaign in Iowa, said he has the support of Dean Kleckner, a former state Farm Bureau president and a party activist, and Pottawattamie County Chairman Jeff Jorgenson.
By contrast, Romney, Perry, Bachmann and former Sen. Rick Santorum have netted endorsements from state lawmakers and local party officials whose own networks could potentially prove beneficial.
So far, Cain has not run television commercials in the state, unlike Bachmann, Perry and Rep. Ron Paul of Texas.
Cain also trails rivals in organizational strength in New Hampshire, site of the first primary on Jan. 10.
He has two paid staff in the state, far fewer than Romney, Perry and former Utah Gov. Jon Huntsman, each of whom has more than 10.
Cain's most prominent New Hampshire supporter to date is Jack Kimball, the former state GOP chairman who was forced out of office last month having lost the confidence of most state officials.
In South Carolina, which hosts the first Southern state caucus, Cain has a staff of four and shows evidence of grassroots support. He won a straw poll of 110 women at a state Federation of Republican Woman meeting last weekend, followed closely by former Speaker Newt Gingrich, Bachmann and Romney.
Perry appears to have the largest organization in the state, and enjoys the support of roughly a dozen state lawmakers as well as one member of the state's congressional delegation, Rep. Mick Mulvaney.
Nationally, Cain also lags several of his rivals in fundraising, based on reports filed through the end of September, the most recent available.
At the time, Perry, the Texas governor, reported cash on hand of $15 million. Romney, the former Massachusetts governor making his second presidential run, reported $14.6 million in the bank.
Cain's cash on hand was $1.3 million, and his filing indicated he was more reliant on small donors - those giving $200 or less - than either Romney or Perry.
While polls are notoriously fickle, particularly before the first ballots are cast in a presidential race, Cain shot up rapidly in recent weeks, largely at Perry's expense, and his aides were eager to circulate the results of a Washington Post survey taken as the sexual harassment controversy was unfolding.
It showed him in a statistical tie for first with Romney, who had 24 percent support to 23 for Cain. Perry had 13, followed by Gingrich with 12.
Seven in 10 Republicans polled said reports of the allegations don't matter when it comes to picking a candidate.
But in a sign of possible danger ahead, the poll found that Cain slipped to third place among those who see the accusations as serious, and Republican women were significantly more likely than men to say the allegations make them less apt to support the businessman. The survey found that support for Cain was basically steady over the four nights of interviewing, though new accusations were surfacing.
In South Carolina, LaDonna Riggs, chairwoman of the Spartanburg County Republican Party, said she had seen nothing so far that would cause party activists to abandon Cain. "You give me some substance to the questions and then we can talk," she said.
"If there's truth to it, then it could hurt him. But right now, it's just allegations," said Cyrus Hill, a 67-year-old retiree from Granger, Iowa. "Allegations aren't going to end him.
Dave Roszak, 51 and a resident of Clive, Iowa, said, "If it turns out he isn't being honest, it will take him down."
Associated Press writers Shannon McCaffrey in Georgia, Tom Beaumont and Phil Elliott in Iowa, Steve Peoples in New Hampshire and Jim Davenport in South Carolina contributed to this story.