Mr. Trump responded, "We're going to do a great job".
"Tourism - I can say this - you're going to go up ten-fold, with the expenditure of no money...."
"Eddie, I have to tell you, you've become extremely famous", said the president, who telephoned from Bedminster, New Jersey, where's he on a working vacation.
North Korean leader Kim Jong-un has threatened to fire missiles at Guam, home to US military bases in the South Pacific, in an escalating war of words over Pyongyang's nuclear-weapons program.
Calvo agrees, saying, "It's paradise". You are safe. We're with you 1,000 percent.
While Trump maintained a lighthearted tone, Guam's Office of Civil Defense started passing out flyers on Friday to help residents prepare for a missile attack from North Korea.
The phone call came shortly after authorities in Guam issued documents advising residents on to respond in the event of an "imminent missile threat". It included information on how to build an emergency supply kit, make an emergency family plan, make a list of potential concrete shelters near your home, and to not look at the flash or fireball because it can blind you.
"They should have had me eight years ago, or at least somebody with my thought process", Trump said.
A video shared by Guam's Office of Civil Defence captured a phone call between Guam's Governor Eddie Baza Calvo and the U.S. president.
"It just looks like a handsome place", Mr. Trump said. We are rock solid, and we have the best in the world by a factor of five.
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.
British Foreign Secretary Boris Johnson on Saturday (Aug 12) blamed North Korea for the stand-off with the United States and said London wants a diplomatic end to the crisis.
Mr. Trump had threatened to rain "fire and fury" on North Korea for any provocation.