The scheme to target the island, a key US military stronghold, was intended to "signal a crucial warning" as "only absolute force" would have an effect on the US leader, the North said.
The declaration came after Trump boasted on Twitter that America's nuclear arsenal was "far stronger and more powerful than ever before".
Earlier, Trump stunned the world with a bold-faced message to leader Kim Jong-Un that appeared to borrow from Pyongyang's own rhetorical arsenal, saying the North faced "fire and fury like the world has never seen".
Last month the North carried out two successful tests of an intercontinental ballistic missile, bringing much of the US mainland within its range.
Trump's "fire and fury" remarks were "a load of nonsense", said General Kim Rak-Gyom, the commander of the North's missile forces, according to Pyongyang's official Korean Central News Agency.
"Sound dialogue is not possible with such a guy bereft of reason," he added in a statement.
The military would complete the Guam plan by mid-August and submit it to Kim Jong-Un for consideration, he said.
They would have a flight time of 17 minutes 45 seconds, travel 3,356.7 kilometres (around 2,086 miles) and come down 30 to 40 kilometres away from Guam, it said -- which would put the impact points just outside US territorial waters.
Japan, which has in the past warned it would shoot down any North Korean missiles that threaten its territory, responded quickly to insist it can "never tolerate" provocations from the reclusive state.
The western Pacific island of Guam is home to US strategic assets including long-range bombers and military jets and submarines, which are regularly deployed for shows of force in and near the Korean peninsula, to Pyongyang's fury.
Professor Yang Moo-Jin of Seoul's University of North Korean Studies said the level of detail in Pyongyang's declaration was unusual.
"The North appears to be saying what it is going to do is within international laws," he told AFP. "Therefore, it cannot be ruled out that the North may translate this plan into reality."
During the Cold War in the 1980s the Soviet Union sent unarmed missiles to come down in the Pacific within 1,000 kilometres of Hawaii.
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