Washington (CNN) -- One of the women who accused Republican presidential contender Herman Cain of sexual harassment released a statement through her lawyer Friday saying that she "stands by" her complaint, which was made "in good faith about a series of inappropriate behaviors and unwanted advances."
There was "more than one incident" of harassment involving Cain and his client over the span of a couple of months in 1999, attorney Joel Bennett said.
Bennett said his client, married for 26 years, will not reveal her identity because "she and her husband see no value in revisiting this matter now nor in discussing the matter any further publicly or privately."
"In fact," he added, "it would be extremely painful for her to do so."
Bennett released the statement after reaching an agreement to do so with the National Restaurant Association, the organization headed by Cain during the time of the alleged harassment. The group has an agreement with the alleged victim that includes a series of confidentiality and non-disparagement provisions.
Dawn Sweeney, the current head of the association, issued a statement confirming that in July 1999, Bennett's client "filed a formal internal complaint, in accordance with the association's existing policies prohibiting discrimination and harassment."
Cain, she noted, "disputed the allegations in the complaint."
Sweeney said the association is prepared to fully release Bennett's client from her confidentiality agreement in the event she wants to disclose additional details.
The controversy has dominated Cain's front-running campaign for the past week. A defiant Cain insists he did nothing wrong, and will not let the issue deter him.
Cain spokesman J.D. Gordon said in response to Bennett's statement that the Cain campaign looks "forward to focusing our attention on the real issues impacting this country -- like fixing this broken economy and putting Americans back to work."
Cain's campaign said earlier Friday it is considering filing a lawsuit against Politico, the news organization which broke the harassment story last Sunday.
A possible lawsuit "is being discussed," Gordon told CNN. Gordon declined, however, to discuss the timetable or legal basis for such a move. Cain and his campaign aides have been highly critical of Politico's use of anonymous sources, among other things.
Politico executive editor Jim VandeHei told CNN he had heard nothing from the Cain campaign, and said the organization "stands confidently behind every story (our) reporters have written on the topic."
Cain has cited strong poll numbers and fund-raising to claim voters know the allegations are a baseless political attack.
"The American people are starting to see through this stuff, and they are sick of gutter politics," Cain declared in a radio interview with conservative commentator Sean Hannity on Thursday. "This will not deter me."
Asked about money paid to two women -- including Bennett's client -- when they left the National Restaurant Association, Cain said in the one case he recalled, it was severance money because accusations of impropriety on his part proved unfounded.
Bennett insisted Friday there was no severance agreement, but rather a financial settlement of the harassment complaint.
Cain on Thursday also repeated his accusation that the campaign of Texas Gov. Rick Perry, a conservative rival for the GOP nomination, was behind the allegations emerging as Cain rose to the top of the polls in the race.
In particular, he noted that a former aide, Curt Anderson, signed on with the Perry campaign shortly before the allegations surfaced in Politico.
"These are the facts. Connect the dots," Cain said, adding that "as more of the information comes out, the more baseless it appears to people."
In an interview Thursday with CNN, however, Perry flatly denied that his campaign had anything to do with the story. He also vowed that he'd fire any staffer if he found out they were "passing on rumors."
"(There is) no apology needed," Perry said. "We found out about this the same time that I suppose the rest of America found out about it. I don't know how to tell it any other way, except I knew nothing about it."
Cain later softened his earlier claim that he told Anderson about one of the allegations against him in a private discussion in 2003. On Thursday, he told Hannity he was "almost certain" the discussion took place.
The allegations have set off a fierce round of claims and counter-claims regarding how the information became public. At the same time, Cain's campaign announced Thursday he has raised $1.2 million this week since the allegations first surfaced on Sunday in a big boost from supporters.
The news appears to have had little impact so far on Cain's standing in the GOP race. An ABC News/Washington Post poll released Friday morning -- the first survey conducted entirely after news of the alleged harassment broke -- showed Cain in a dead heat with former Massachusetts Gov. Mitt Romney atop the GOP field.
According to the poll, 24% of Republicans and independents who lean toward the GOP now say they support Romney, compared with 23% for Cain. Romney and Cain have been neck-and-neck in most major national surveys over the past month.
What exactly transpired during the alleged harassment incidents remains unclear. Asked by Hannity if he ever made flirtatious comments to female subordinates or comments such as "you look hot" or anything, Cain replied: "No, no, no, I didn't."
As a business leader, he said, he "learned a long time ago" not to comment on a woman's appearance or make any kind of personal comment unless he was "really, really comfortable" with a colleague. Cain told HLN earlier this week that he has never committed sexual harassment "in (his) entire career. Period."
For his part, Anderson denied in a CNN interview Thursday that he was responsible for leaking the allegations.
Anderson, who worked on Cain's unsuccessful 2004 U.S. Senate campaign in Georgia and now is a consultant to Perry's campaign, insisted Cain never told him about the accusations.
"It's hard to leak something you don't know anything about," he said. "I don't have any knowledge of any of this and, you know, it's just not true."
Later, Cain's chief campaign strategist, Mark Block, said he accepted Anderson's denial, and wanted to move on from the controversy that has dogged his candidate all week.
"Until we get all the facts, I'm just going to say that we accept what Mr. Anderson has said, and we want to move on with the campaign," Block told Fox News. Block had earlier called for Perry to apologize to Cain for allegedly leaking the harassment allegations to the media.
Politico first published a report late Sunday claiming that two female employees at the National Restaurant Association accused Cain of inappropriate behavior during his tenure as head of the organization. The women, according to Politico, each received separation packages in the five-figure range.
The package for one of the women totaled between $32,000 to $37,000 -- approximately equivalent to her annual salary at the time, according to a former National Restaurant Association employee who knows one of the accusers.
"The workplace (had become) uncommunicative," the former employee told CNN. "They didn't give her work. She didn't interact with people."
The New York Times previously reported that one of the packages totaled $35,000. On Thursday, Politico reported the other package was for $45,000.
Cain criticized the Politico report in Thursday's interview, saying the Politico reporters never showed him any documentation or talked to the women who allegedly made the claims. When a Politico reporter was asked on CNN whether another campaign tipped him to the story, he refused to answer, Cain noted.
"I didn't know there were so many women named 'anonymous' in America, frankly," Cain joked in Thursday's interview about the lack of details about his accusers. Politico editor-in-chief John Harris told CNN the organization is following ordinary media standards by protecting its sources.
Cain has provided differing accounts of the allegations this week, raising further questions about what happened and the ability of the candidate and his campaign to deal with the controversy. While Cain's campaign was first approached by Politico 10 days before the story was first published, the candidate said he was only remembering many details of the incident on Monday.
Cain has seized on the uproar as an example of alleged liberal media bias.
On Wednesday, Cain's campaign called a report that a third former employee had claimed that he had engaged in inappropriate behavior an example of "baseless allegations."
"He has never acted in the way alleged by inside-the-Beltway media, and his distinguished record over 40 years spent climbing the corporate ladder speaks for itself," said J.D. Gordon, a Cain campaign spokesman. "Since his critics have not been successful in attacking his ideas, they are resorting to bitter personal attacks. Mr. Cain deserves better."
In the Hannity interview, Cain accused his critics of engaging in the politics of personal destruction, and he insisted his candidacy would survive the maelstrom.
He blasted what he called a "vicious liberal attack on me," saying the false accusations are because opponents can't coherently challenge his message and want to "intimidate other black conservatives to not go public."
So far, Cain has only released details about one of the allegations, saying it involved him gesturing to one of the women that she was the same height as his wife -- about 5 feet tall -- and came up to his chin.
Bennett has not indicated which of the alleged victims he represents, though he said his client is taller than 5 feet. He said earlier this week that his client is "happily married."
For his part, Cain has said he has no recollection of a second incident. According to Politico, however, one of the allegations involves an "unwanted sexual advance" at a hotel room in Chicago.
An independent group trying to help Cain released a web video Friday defending him against the harassment allegations and harshly criticizing media coverage of the story.
The video, by a super political action committee called the 9-9-9 Fund, includes clips of conservative hosts, including Rush Limbaugh. It also uses television clips of liberal pundits attacking Cain, as well as the famous clip of Supreme Court Justice Clarence Thomas calling his grilling during his confirmation hearings two decades ago "a high-tech lynching."
The video ends with the onscreen message, "Don't let the left do it again."
CNN's Brian Todd, Gloria Borger, Dugald McConnell, Joshua Levs, Kevin Bohn, Mark Preston, Jim Acosta, Phil Gast and Paul Steinhauser contributed to this report.