Andersen Air Force Base on Guam is where the US keeps its B1-B bombers deployed to the Asia Pacific.
The North is apparently unnerved by the frequent appearance of US bombers, aircraft carriers and nuclear submarines in the vicinity of its territory.
During the hour-long phone call on Monday, Moon and Trump said they would continue cooperating to rein in North Korea, particularly ahead of a regular joint military drill set for late August, South Korean presidential office spokesman Park Su-hyun told a media briefing.
The Strategic Force of the Korean People's Army said in a statement that it's considering the use of intermediate-range ballistic missile Hwasong-12 for an "enveloping fire" at the areas in the vicinity of Guam.
"This grave situation requires the KPA to closely watch Guam, the outpost and beachhead for invading the DPRK, and necessarily take practical actions of significance to neutralize it".
"The execution of this plan will offer an occasion for the Yankees to be the first to experience the might of the strategic weapons of the DPRK closest", the spokesman said.
"North Korea's missiles and nuclear facilities are dispersed and hidden throughout the country's mountainous terrain".
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A note was also found, along with the object which stated "Dujana ki shahaadat ka badla abb Hindustan ko chukaana padega". Senior Home Department officials said an alert has been sounded across the state and security has been upgraded.
Six bombers are now in position in Guam, 2,100 miles away from North Korea.
Guam, a USA island territory, is a popular tourist destination.
Nationalists claim that it is because of the USA military that the island attracts potential threats.
According to the Pentagon's Missile Defense Agency, the missile defense system, which entails a tracking radar, launcher, interceptor missiles and an integrated fire-control system, has a 14 out of 14 test intercept success rate since 2006. Guam's Homeland Security Advisor George Charfauros told CNN the U.S. "routinely uses" Aegis-equipped warships around the island chain of the Marianas, of which Guam is the largest.
The Pacific island of Guam remained calm a day after the apocalyptic threats from Korea.
Guam is about 2,100 miles (3,380 kilometers) southeast of Pyongyang and 3,800 miles (6,115 kilometers) west of Honolulu in the Pacific Ocean.
Though local officials downplayed any threat, people who live and work on the island, which serves as a launching pad for the US military, said Wednesday they could no longer shrug off the idea of being a potential target. Since then he has launched foreign bureaus for CNSNews.com in Jerusalem, London and the Pacific Rim.