The tiny Pacific Ocean island is a USA territory 2,200 miles southeast of North Korea with about 160,000 residents and an Air Force base, a Navy base and a Coast Guard station.
Many across the island say they feel assured and protected by the military.
For years, North Korea has claimed Guam is within its missiles' striking distance, making furious statements each time when the USA flew powerful bombers from the island's air base to the Korean Peninsula.
The possibility of a nuclear confrontation is considered remote but worldwide alarm has been escalating in recent days.
North Korea's statement was released just hours after Trump warned the Kim Jong-un regime that it "will be met with fire and fury like the world has never seen" if it does not stop threatening the US, Efe news reported. "For now, we advise the community to remain calm, remember that there are defenses in place for threats such as North Korea and to continue to remain prepared for all hazards".
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George Charfauros, Guam's homeland security adviser, said the current defense system is capable of defending the island.
Shortly after Trump made his remarks, North Korea said it was "carefully examining" the idea of a missile strike on Guam, a U.S. Pacific territory.
This is not the first time that North Korea threatened Guam. An attack or threat to Guam is a threat or attack on the United States.
"They believe that we are not true USA citizens, when we do have plenty of Chamorro people going into the USA military and serving for their country and dying for their country", he said. For years, North Korea has claimed Guam is within its missiles' striking distance, making furious statements each time when the US flew powerful bombers from the island's air base to the Korean Peninsula.
Guam is about 2,100 miles (3,380 kilometres ) southeast of Pyongyang and 3,800 miles (6,115 kilometres ) west of Honolulu in the Pacific Ocean.