Mr. Cain spent the day in television interviews and news briefings attempting damage control.
He maintained that he had been falsely accused and that investigations at the association corroborated that.
Mr. Cain’s explanations and gaps in the story made it hard to determine the impact of the revelations on his prospects in states like Iowa, whose caucuses are two months away.
Mr. Cain said to the National Press Club in Washington that “I am unaware of any sort of settlement” related to the accusations, which he called “a witch hunt.” In an interview with Greta Van Susteren of the Fox News Channel later, he acknowledged that “there was some sort of settlement or termination,” worth “maybe three months’ salary.”
Politico detailed incidents between Mr. Cain and two women on the staff that led to settlements. The incidents included “conversations allegedly filled with innuendo or personal questions of a sexually suggestive nature.”
In interviews, two people affiliated with the restaurant group said they knew of the second female employee, and she had received a payment related to harassment accusations against Mr. Cain during his tenure as the association’s chief executive.
They said the second woman similarly complained about what she said had been Mr. Cain’s inappropriate conduct. One said she had been taken aback by one interaction while they were traveling. He said he believed harassment was not the only issue involved in the woman’s termination package.
The restaurant association declined to comment on what it termed “personnel matters that allegedly took place nearly 15 years ago.”
With only scant details from the encounters available so far, the already tricky business of divining how the allegations may affect Mr. Cain’s rising political fortunes was made all the more difficult on Monday.
His candidacy has been enigmatic from the start, and his rise to the top in national polls and in surveys of early voting states has upended expectations in the Republican contest. Aides to rivals including former Gov. Mitt Romney of Massachusetts, who shares top billing with him in polls, and Gov. Rick Perry of Texas, who trails them, have expressed skepticism that Mr. Cain’s campaign can go the distance but have been unable to ignore his strong marks from voters or the appeal of his blunt policy prescriptions.