Donald Trump has praised Newt Gingrich for an "amazing interview" in which the former speaker told Fox News Channel host Megyn Kelly that she is "fascinated with sex".
The heated exchange on Ms Kelly's programme on Tuesday night ended with her suggesting Mr Gingrich take some time for anger management.
The confrontation revived dormant ill will with the Trump campaign towards Ms Kelly that dates to his anger at her asking him at a pre-Republican primary debate more than a year ago to account for statements about women.
Mr Trump boycotted a later Republican debate when Fox would not remove Ms Kelly as a moderator.
Mr Gingrich attended Mr Trump's dedication of his new hotel in Washington on Wednesday, and the presidential candidate recognised him in the audience.
"Congratulations," Mr Trump said. "That was an amazing interview last night ... We don't play games, Newt."
For his part, Mr Gingrich said "that's just the business" when he was asked by reporters about the exchange.
Mr Gingrich, a Fox contributor being interviewed as a Trump surrogate, and Ms Kelly began arguing when she asked him about allegations by several women that the Republican presidential candidate had groped them or kissed them against their will.
"You are fascinated by sex and you don't care about public policy," Mr Gingrich said.
"Me? Really?" Ms Kelly replied with a slight laugh.
Mr Gingrich interrupted Ms Kelly when she began a statement by saying "if Donald Trump is a sexual predator".
He accused her of slapping that label on Mr Trump.
Ms Kelly said she is not taking a position on it, "unlike you".
Mr Gingrich asked Ms Kelly whether she wanted to comment on whether the Hillary Clinton ticket has a relationship to a sexual predator.
Ms Kelly said her programme had covered past allegations made against former president Bill Clinton and noted that he - unlike Mr Trump - was not a current candidate for president.
"I want to hear your words: Bill Clinton, sexual predator," Mr Gingrich said.
"I dare you. Say 'Bill Clinton, sexual predator'."
Ms Kelly ignored his request.
After some more back-and-forth, Ms Kelly ended the segment.
"We're going to have to leave it at that and you can take your anger issues and spend some time working on them, Mr Speaker," she said.
The exchange was a popular topic on social media, where - depending on the point of view of those posting - Mr Gingrich either "schooled" Ms Kelly or vice versa.
Mr Trump's social media director, Dan Scavino Jr, tweeted that the exchange showed Ms Kelly "is totally biased against Mr. Trump and not very smart".