“I will be putting forth the nominee next week; it will be a woman,” Mr. Trump told supporters at an outdoor rally at an airport in Fayetteville, N.C. “I actually like women much more than I like men.”

He also indicated that he would push for a swift vote on his nominee, without regard for the results of the November election.

“It says the president is supposed to fill that seat, right?” he said, referring to the U.S. Constitution. “And that’s what we’re going to do, is fill that seat.”

“Fill that seat!” members of the audience chanted to the president’s satisfaction. “You said it better than I can say it,” he said, suggesting that his campaign make T-shirts with the slogan.