HAGATNA, Guam — If there’s one thing that Guam does not have to worry about while the tiny island is in the nuclear cross hairs of North Korea, it’s tourism, President Trump told the island’s governor in a phone call made public on Saturday.

The threat by North Korea’s leader, Kim Jong-un, to create “an enveloping fire” around the tiny United States territory in the Western Pacific will bolster Guam tourism “tenfold,” Mr. Trump said in the recorded conversation with Gov. Eddie Calvo.

The recording was put on the Republican governor’s Facebook page and other social media accounts.

Mr. Trump said: “I have to tell you, you have become extremely famous all over the world. They are talking about Guam; and they’re talking about you.” And when it comes to tourism, he added, “I can say this: You’re going to go up, like, tenfold with the expenditure of no money.”