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Donald J. Trump has attracted enormous attention for his proposal to temporarily bar Muslims from entering the United States. But on Monday he said he was “happy” that London had elected its first Muslim mayor and suggested that the new official would be among the exceptions to his proposal.

“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.”

Mr. Trump has been criticized for his proposed ban, which he announced soon after the terrorist attacks in Paris in November that killed 130 people.

Mr. Khan, in an interview with Time magazine after his election, criticized Mr. Trump’s approach to Muslims and said he planned to visit the United States before the inauguration.

“If Donald Trump becomes the president I’ll be stopped from going there by virtue of my faith, which means I can’t engage with American mayors and swap ideas,” Mr. Khan said.

