According to a video tweeted by the Guam News on Friday, Calvo while talking to Trump via an office phone switched the call to speaker phone to enable viewers hear the conversation clearly, Xinhua news agency reported.
Guam is telling its residents what to do if North Korea launches a missile attack at the USA territory, but is also calling for calm.
"So, with all the criticism going on over there for a guy who's doing what's positive, we need a president like you".
Before speaking to Mr Calvo, Mr Trump told reporters in New Jersey that he believed Guam would be "very safe" and threatened North Korea with "big, big trouble" if it launched an attack.
US, North Korea have engaged in backchannel diplomacy
Trump again on Friday warned North Korea against following through on a threat made Wednesday to fire a weapon against the U.S. "He has genuine concern about the direction of events in North Korea".
"You've become extremely famous", he told Mr Calvo of the global news coverage following North Korea's threat. All over the world they're talking about Guam and they're talking about you.
"When (Russian President Vladimir) Putin says that, you know, he didn't interfere in our election - he was lying. I'll talk to you anytime you need, and again, it looks like just a handsome place".
Calvo agrees. "It's paradise, " he says.
Hawaii has also sought to prepare residents for the threat of a nuclear missile attack from North Korea, while stressing that the risk of a strike is low.
"If an attack warning is issued, take cover as quickly as you can, under concrete structure or below ground if possible", the sheet adds.
Trisha Paytas quits 'extremely unhealthy' Celebrity Big Brother
She has said she regrets leaving the show, telling followers: "Like everything else in my life, I **** things up for myself". She will fly home to the U.S. on Tuesday, telling fans on YouTube that it was earliest available flight she could get home.
Referring to an "imminent missile threat", it includes advice like: "Do not look at the flash or fireball - it can blind you".
"Don't worry about a thing and they should have had me eight years ago, or at least somebody with my thought process, because that was the time", Trump said.
Gen. Restituto Padilla Jr. said the possibility that the Philippines could be hit if North Korea proceeded with its threat was "remote".
Padilla made the statement after the North Korean Strategic Force of the Korean People's Army said on Thursday it was "seriously examining a plan" to fire a missile near Guam.
Trump says he hopes not to have to use U.S. nukes
She said Tillerson and Mattis had a good relationship and that Tillerson had not spoken about US military capabilities. Burr has indicated that he is limiting his trips to the White House during the politically sensitive investigation.