Mr Calvo, meanwhile, responded: "I have never felt more safe or so confident with you at the helm".
"And I also want to remind the national media that Guam is American soil, and we have 200,000 Americans in Guam and the Marinas", he said.
President Trump on Friday assured the governor of Guam that the White House is "with you 1,000 percent" in the face of a threat from North Korea - and then told the governor that he's becoming famous and predicted the attention would boost tourism "tenfold" in the USA territory.
Trump went on to congratulate Calvo for "becoming extremely famous", adding, "All over the world they're talking about Guam".
A video shows Gov. Eddie Baza Calvo laughing and joking with the president as they discuss everything from the readiness of the USA military to tourism.
"Don't worry about a thing", Trump said.
He told Calvo: "You notice that he hasn't spoken recently?"More news: Trump Takes Credit For Nuclear Arsenal Improvments By Obama Administration
North Korea said earlier this week it would complete plans to launch missiles into the waters near Guam by mid-August.
If a warning is issued, Guam residents should take cover quickly - in a concrete structure, preferably underground - and stay there until instructed otherwise, according to the fact sheet titled "Preparing for an Imminent Missile Threat".
Trump, and Chief of Staff General John Kelly, phoned Guam's governor Eddie Baza Calvo to assure him that the people of the country are safe and that the president is behind the them "1000 percent". They should have had me eight years ago, somebody with my thought process, because that was the time. Governor Eddie Calvo during a press briefing on Friday told everyone to remain calm and enjoy the weekend. It just looks like a handsome place.
He concluded, "May God bless the people of Guam, and may God bless America". We are rock solid, and we have the best in the world by a factor of five.
Tensions between North Korea and the USA have escalated this week amid increasingly heated rhetoric between Trump and North Korean leader Kim Jong Un.
Mr. Trump plans to meet Mr. Xi later this year in what the White House called "a very historic event".