Donald J. Trump interrupted a promotion for his new hotel in Washington to shower praise on Newt Gingrich for confronting the Fox News host Megyn Kelly on Tuesday night, when the former House speaker said in an interview that she was “fascinated with sex” in her reporting on Mr. Trump’s treatment of women.

Speaking at a gold-gilded lectern at the Trump International Hotel on Pennsylvania Avenue on Wednesday, Mr. Trump pointed a finger toward Mr. Gingrich, who was in the audience at the hotel ribbon-cutting.

“Congratulations, Newt, on last night — that was an amazing interview,” Mr. Trump said. “We don’t play games, Newt, right? We don’t play games.”

Ms. Kelly has been a frequent target of Mr. Trump ever since she was a moderator at the first Republican primary debate in August 2015 and asked him about his past misogynistic comments.