Herman Cain says he'd be willing to take a lie detector test to prove he's being truthful when he says he has never behaved inappropriately with anyone.
But he says he won't submit to such an examination without a good reason.
The Republican presidential candidate has been battling allegations of sexually inappropriate behavior involving four women. The accusations date to his time as head of the National Restaurant Association in Washington.
At a news conference Tuesday, Cain issued fresh denials of the allegations. He said a Chicago-area woman's story that he groped her in mid-1997 "simply did not happen."