In appearance on David Letterman's "Late Show" airing Friday night, the former pizza executive is again denying any impropriety during his time running the National Restaurant Association in the 1990s.
Four women have come forward with allegations against Cain. He has repeatedly denied the allegations, which have dogged his campaign.
Cain instead is trying to talk about his presidential bid and his 9-9-9 tax plan.
In excerpts from the show released in advance, Cain jokes that Letterman seemed to be trying to talk him out of his presidential bid with tough questions about the challenges facing the presidency.