“I’m glad he didn’t run him over,” Mr. Watters said. “Also, I’m going to be taking a vacation with my family, so I’m not going to be here tomorrow and Friday. But I’ll be back on Monday, so try not to miss me too much.”
“Saturday also?” asked Kimberly Guilfoyle, a co-host.
“Yes, and K.G. is going to be hosting ‘Watters’ World’ on Saturday,” he said, referring to Ms. Guilfoyle.
Barely missing a beat, the focus then shifted to the birth of a two-toed sloth at the Memphis Zoo.
Mr. Watters’s highly scrutinized joke came during Tuesday’s show as the hosts discussed footage of Ms. Trump being jeered on stage in Berlin while she was speaking on a panel about female entrepreneurship.
“It’s funny, the left says they really respect women, and then when given an opportunity to respect a woman like that, they boo and hiss,” he said.
Then he added with a grin: “So I don’t really get what’s going on here, but I really liked how she was speaking into that microphone.”
On Wednesday, after the clip had been shared widely on social media, Mr. Watters said in a statement that the comment had not been sexual innuendo, as critics perceived it to be.
“During the break we were commenting on Ivanka’s voice and how it was low and steady and resonates like a smooth jazz radio DJ,” he said in a statement. “This was in no way a joke about anything else.”
It’s an especially inopportune time for any whiff of sexism at Fox News. Mr. O’Reilly, among the network’s biggest stars, left the network last week over accusations of sexual harassment and inappropriate behavior.
Its former chairman, Roger Ailes, was forced out last year after several female employees came forward with sexual harassment claims. Two more women, Julie Roginsky and Alisyn Camerota, lodged new complaints against Mr. Ailes this month.
Mr. Watters, a protégé of Mr. O’Reilly, has ascended at Fox News despite occasionally attracting his own firestorms, including a heavily criticized segment in which he leaned on Asian stereotypes. In March, he scored an interview with President Trump.