“There will always be exceptions,” Mr. Trump said when asked in an interview on Monday how his proposed ban would affect London’s mayor, Sadiq Khan.

“I was happy to see that,” Mr. Trump said of Mr. Khan’s election. “I think it’s a very good thing, and I hope he does a very good job because frankly that would be very, very good.”

Asked why, Mr. Trump said, “Because I think if he does a great job, it will really — you lead by example, always lead by example. If he does a good job and frankly if he does a great job, that would be a terrific thing.”