Washington (CNN) -- A defiant Herman Cain on Thursday continued to deny allegations of sexual harassment in his past and said he won't be deterred by the controversy that has dominated his front-running campaign for the Republican presidential nomination.
Citing strong poll numbers and fundraising, Cain said voters knew that the allegations were 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. "This will not deter me."
Asked specifically about money paid to two women when they left the National Restaurant Association while he headed the organization in the late 1990s, Cain said in the one case he recalled, it was severance money because any accusations of impropriety on his part proved unfounded.
Cain 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 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 a report Sunday by 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, reiterating an earlier comment from campaign communications director Ray Sullivan. 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.
Meanwhile, one of two women who reportedly accused Cain of sexual harassment could issue her first statement on what happened as early as Friday.
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.
Earlier Thursday, Anderson denied in a CNN interview 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 against Cain and other Republican contenders, insisted that Cain never told him about the accusations.
"It's hard to leak something you don't know anything about," he said. Asked directly about the conversation Cain claimed they had eight years ago, Anderson 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, told Fox News that 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," said Block, who had earlier called for Perry and his campaign to apologize to Cain for allegedly leaking the sexual harassment allegations to the media.
Politico's report Sunday alleged that two female employees at the National Restaurant Association accused Cain of inappropriate behavior during his tenure as head of the organization in the late 1990s. The women, according to Politico, each received separation packages in the five-figure range.
One of the packages totaled $35,000 -- equivalent to that staffer's annual salary, according to the New York Times. 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's editor-in-chief, John Harris, responded to Cain's criticisms by noting his publication followed usual standards in protecting sources and divulging information.
"We don't share our sources," Harris told CNN.
Cain has provided differing statements on the allegations this week, raising further questions about what happened and the ability of the candidate and his campaign to deal with the controversy.
A former businessman who touts himself as a political outsider, Cain has run an unorthodox campaign that made him an early choice of conservatives seeking an alternative to the more moderate Mitt Romney, a former governor of Massachusetts.
Republican strategist Ed Rollins said Thursday that Cain's campaign lacks the usual elements to deal with such controversies that inevitably arise.
"They take great pride in not being a real campaign," Rollins told CNN. "They don't have a war room. They don't have a response team."
Rollins, until recently a chief adviser to Rep. Michele Bachmann of Minnesota -- another of Cain's rivals in the presidential nomination race -- noted that Politico first asked the Cain campaign about the sexual harassment allegations 10 days before running the story."
"Ten days is a lifetime in politics," Rollins said. "They should have been prepared for this."
In the CNN interview, Anderson spoke highly of his former employer and suggested that the pressure of the sexual harassment story was getting to the former businessman.
"Candidates, when they get into a firestorm like this, have sometimes come unraveled," Anderson said. "It seems to me that they're kind of grasping at straws and fishing around trying to figure out what to do, how to get out of this."
Saying he was "disappointed" that Cain "tried to use me as a pawn to try to get out of this mess he's in," Anderson said he was "not going to use that to discolor everything I know about the guy."
On Wednesday, Cain's campaign called a report that a third former employee claimed he 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."
Prompted by Hannity -- for whom Cain has filled in as host of the radio show on occasion -- Cain also said the media was going harder on him that it did on President Barack Obama's links to Bill Ayers, who helped found the Weather Underground revolutionary group that conducted a bombing campaign against the Vietnam War.
A Quinnipiac University national poll this week showed Cain leading the GOP field with 30% support among registered Republicans, compared with 23% for Romney. The survey, however, was conducted almost entirely before news of the allegations came out.
During the week, Cain's account of what happened more than a decade ago changed from day to day.
On Monday, Cain forcefully denied all of the charges and said he was "not aware of any (legal) settlement." Later, he changed his tune, saying he did in fact know about a "separation agreement" in one of the cases.
In the interview Thursday, Cain said there wasn't any change in his story, because as a businessman, he considered a settlement a legal matter while an agreement would involve a lesser issue.
The candidate told HLN's Robin Meade on Tuesday that the agreement provided one of his accusers "in the vicinity of three to six months' severance pay." The payment was "not outside our guidelines for what most people get ... when they leave the Restaurant Association involuntarily," he claimed.
While the Cain campaign had first been approached by Politico 10 days before the story was first published, the candidate himself said he was only remembering many details of the incident on Monday.
Cain continued to vehemently deny the allegations, telling HLN: "I have never committed sexual harassment in my entire career. Period."
Meanwhile, an attorney representing one of the alleged harassment victims sent a draft statement regarding his client to the National Restaurant Association on Thursday to seek its approval.
"I will be asking the association to allow us to release the public statement without violating the confidentiality and non-disparagement provisions of the 1999 settlement agreement," said the attorney, Joel Bennett.
He later told CNN he hopes to be able to release the one-page statement on Friday. The statement will not include his client's identity because she is trying to "remain private," he said. The draft statement, according to Bennett, is a summary of "what she did and why she did it" but the draft does not include specifics about any incidents or about any settlement.
The association said it would respond to the proposed statement on Friday.
Cain had harsh criticism for Bennett, accusing him of trying to drum up publicity for himself to "make a lot of money." Bennett later denied Cain's accusation, noting he had turned down multiple requests for television interviews.
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 did not indicate which of the alleged victims he represents, though he said his client is taller than 5 feet. He said the 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.
Separately, an Oklahoma Republican political consultant told CNN Wednesday he personally witnessed Cain demonstrate inappropriate conduct toward a female employee during Cain's tenure as head of the National Restaurant Association. Chris Wilson first made the charge earlier in the day in an interview with KTOK, an Oklahoma radio station.
"To be clear, and you can ask any of the reporters covering this story, I had nothing to do with leaking this in any way, and I've never discussed or shared this story with any of my clients -- period," Wilson told CNN.
On Thursday, Cain rejected Wilson's account as part of the attack strategy against his campaign, with the Georgia Republican claiming -- without offering specifics -- that Wilson "is just trying to help out the Perry campaign."
Wilson is currently doing polling for a political action committee supporting Perry's bid, but the group is independent of the campaign and by law cannot coordinate with it.
CNN's Brian Todd, Gloria Borger, Alan Silverleib, Joshua Levs, Kevin Bohn, Mark Preston, Jim Acosta, Phil Gast and Paul Steinhauser contributed to this story.