LONDON — It looked for all the world like a boardroom scene from “The Apprentice,” with President Trump appraising the candidates to succeed Prime Minister Theresa May, even as she stood by his side at a news conference on Tuesday.

Boris Johnson? “I’ve liked him for a long time.”

Jeremy Hunt? “I know Jeremy, I think he’d do a very good job.”

Michael Gove? The president, at a loss, playfully turned to Mr. Hunt in the front row: “Would he do a good job, Jeremy? Tell me.”

And then, as if slipping off-camera to interview the contenders, Mr. Trump sought a series of meetings with some of those same lawmakers, holding out his endorsement for whoever would remake the Conservative Party in his blustering, bare-knuckled image.