The president responded, “You just went to 110, I think.”
Efforts to reach the White House on Saturday for comment were not immediately successful.
Guam’s $5 billion economy is fueled mainly by tourism and the United States military, which occupies about 30 percent of the island and is looking to expand. The island, roughly the size of Chicago and home to about 160,000 people, is about 2,200 miles southeast of North Korea.
The conversation, in which both men praised each other, differed drastically from Mr. Trump’s contentious calls with leaders of Australia and Mexico in the early days of his administration. Transcripts of those calls were leaked this month.
“We are with you 1,000 percent,” Mr. Trump said in the call to Mr. Calvo, who invited the president to the island. “You are safe. We’re with you 1,000 percent.”
Mr. Trump added of Guam: “It just looks like a beautiful place.”
Mr. Trump had threatened to rain “fire and fury” on North Korea for any provocation. Alluding to Mr. Kim, he told the governor, “You notice he hasn’t spoken recently. He doesn’t talk so much anymore. We’ll see how it all works out.”
He added: “This is between you and I. But you don’t talk like they talk. You can’t do that. You can’t do that with people like us.”
While Guam has generally been calm about the escalating threats of a missile attack, some were not thrilled by the tone of the conversation between the two men.
“Listening to that call left me feeling disgusted,” said Andrea Nicole Grajek, a local artist from Dededo village. “I was so shocked I was actually crying. They’re leaders discussing a rise in fame and tourism, while the world is watching our island carefully to see if we’ll still be here tomorrow.”
The threats of possible aggression against Guam — often referred to as the “tip of the spear” — have become a focal point of debate about the presence of United States military forces on the island.
Activists who are advocating Guam’s independence from the United States argue that the presence of the military installations has made the island a magnet for attack. Others contend that the presence of the United States defense system is necessary, given the threats in the region.
“I think Guam is being used as a kind of pawn in this game,” said Robert Underwood, president of the University of Guam. “I think it’s like our role in life.”
Mr. Underwood, a former Guam delegate to Congress, said Guam should find a way to take advantage of its relationship with the federal government if the island continues as the platform to project the United States’ military power in Asia.
“I think we should get more out of this relationship than what we are getting now,” he said.
Mr. Calvo, however, told Mr. Trump that he had “never felt more safe or so confident than with you at the helm. So, with all the criticism going on over there from a guy who is being targeted, we need a president like you. So I’m just so thankful. I’m glad you’re holding the helm.”
Mr. Trump responded: “We’re going to do a great job. You don’t have to worry about a thing. They should have had me eight years ago, somebody with my thought process.”
He added, “And frankly, you could’ve said that for the last three presidents.”