Texas Gov. Rick Perry, on the other hand, said Cain has to address them.
Gingrich, speaking Tuesday at a town hall meeting in Greenville, S.C., said he has been in Cain's situation, with a campaign apparently crumbling, The Atlanta Journal-Constitution reported. He said he would not be ahead in the polls now if he had listened to those telling him to give up.
"First of all, as somebody that most of you said was dead in June, I am not in a position where I am going to say to any candidate that they don't have the right to compete," Gingrich, who has called Cain a good friend, told reporters. "Herman Cain has to do what he thinks is best and what he thinks is best for his family."
Gingrich is the candidate currently vying with former Massachusetts Gov. Mitt Romney for the top spot in the polls, a position formerly held by Cain and before that by Perry. He would not speculate on whether Cain's supporters might turn to him.
Perry took a harder line in an appearance Wednesday on Fox News.
"He needs to address the allegations and if they're true he has to address that with the people of this country," Perry said.
Four women have accused Cain of past sexual harassment and a Georgia woman says she and Cain had a 13-year sexual relationship.
Notable deaths of 2014 [PHOTOS]