The Republican presidential hopeful called a news conference in Arizona Tuesday afternoon to address the ongoing scandal that has sidetracked his campaign and overshadowed the entire GOP nominating race less than two months before the first votes are cast.
Cain focused initially on the newest claims from Sharon Bialek. He said when he watched her news conference Monday, he did not even recognize her, and that her account of inappropriate sexual conduct "simply didn't happen."
At one point Cain called the Chicagoan a "troubled woman," claiming that she was put forward by the "Democrat machine."
"We are not going to allow Washington or politics to deny me the opportunity to represent this great nation. And as far as these accusations causing me to back off, and maybe withdraw from this presidential primary race -- ain't gonna happen," he said.
He later acknowledged he had no evidence to directly link any of his rivals, Democratic or Republican, to orchestrating the crisis in his campaign.
In response to a reporter's question, Cain said that he "absolutely would" subject himself to a lie detector test to clear his name.
"But I'm not going to do that unless I have a good reason to do that," he said. "I believe that the character and integrity of a candidate running for president should come under a microscope -- with facts, not accusations."
Cain also fielded questions about new statements from a previously anonymous accuser, Karen Kraushaar, whose claims against Cain were the subject of the initial Politico story.
Kraushaar, 55, is now a communications director at the Treasury Department, and is a registered Republican who identifies as an independent, according to an NPR report.
She left her job at the National Restaurant Assn. in 1999 after she complained of sexual harassment by Cain, who was the association's president and chief executive from 1996 to 1999.
When she left the job, Kraushaar received a cash payment and signed an agreement with the association that barred her from discussing the matter. The association indicated willingness to release her from the agreement last week at the request of her lawyer, Joel Bennett. But Kraushaar did not want to go public at that time.
Cain said Kraushaar's complaint was "found to be baseless" and treated as a personnel matter.
"When she made her accusations, they were found to be baseless and she could not find anyone to corroborate her story," Cain said. "The restaurant association handled it."
Bennett, Kraushaar's attorney, disputed that claim in an interview Tuesday night with MSNBC's Al Sharpton.
"I have never seen any findings on the complaint that she filed," Bennett said. "So no body of evidence has ever been presented to me that her complaints were baseless."
As he did in an earlier interview, Cain asked the media to avoid drawing his family further into the story, saying some relatives have been "stalked" by reporters.