In an appearance Friday on David Letterman's "Late Show," the former pizza executive again denied any impropriety during his time running the National Restaurant Association in the 1990s.
Several women have come forward with allegations against Cain. He has repeatedly denied the allegations, which have dogged his campaign.
During the interview Letterman says to Cain: "These statements are all false? All of these women are lying? They're all lying?"
"Yes," replies Cain. "They are."
During the show, Cain jokes that Letterman seems to be trying to talk him out of running for president with tough questions about the challenges facing the presidency.