North Korea says it will have a fully developed plan for striking Guam with intermediate range missiles by mid-August.
A state media report suggests the US territory could be attacked by four missiles - and Kim Jong Un will be able to decide whether to proceed within days.
The rockets would land in waters about 18 to 25 miles away from Guam, an island that is home to about 163,000 people - as well as a US military base.
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President Trump has warned North Korea that it will be met with "fire and fury" if it issues any more threats - claims that Pyongyang have described as a "load of nonsense".
The Korean Central News Agency (KCNA) also wrote: "Sound dialogue is not possible with such a guy bereft of reason and only absolute force can work on him."
Earlier on Wednesday, US defence secretary James Mattis had urged North Korea to stop any actions that "would lead to the end of its regime and the destruction of its people".
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Mr Mattis warned the US and its allies would win any arms race or conflict with the rogue state - and called on Mr Kim's regime to "stand down its pursuit of nuclear weapons".
American officials now believe North Korea has successfully made a miniaturised nuclear warhead that can fit inside one of its intercontinental ballistic missiles, according to a Washington Post report.
Recent tests of the missiles have drawn worldwide condemnation and led to fresh UN sanctions against North Korea.
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US secretary of state Rex Tillerson has said Mr Trump had delivered such a stark message to Pyongyang because Mr Kim "doesn't seem to understand diplomatic language".
He explained that the President wanted to "avoid any miscalculation" by North Korea and make it clear that the US has "the unquestionable ability to defend itself".
North Korea says it is going to continue closely watching the speech and behaviour of the US.