|28 July: North Korea launches intercontinental missile|
The threat came hours after President Donald Trump told Pyongyang that any threat to the US would be met with "fire and fury" .
A spokesman for the Korean People's Army said the strike plan would be "put into practice in a multi-current and consecutive way any moment" once Kim Jong Un makes a decision.
He added that "enveloping fire" would be used to contain major US military bases on the island territory in the western Pacific Ocean - including the Anderson Air Force Base.
KCNA, Pyongyang's state-run news agency, also carried a statement from a different military official which said North Korea may carry out a pre-emptive operation if the US shows signs of provocation.
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Guam's governor, Eddie Calvo, has said there is no change in the territory's threat level, and has reassured locals that several layers of defence are strategically placed to protect it.
He added that Guam is "not just a military installation", but American soil with American citizens.
US Secretary of State Rex Tillerson said President Trump delivered his message in the way that he did because the North Korean leader "doesn't seem to understand diplomatic language".
Speaking on his way to Guam, Mr Tillerson said Mr Trump wanted to "avoid any miscalculation" by Pyongyang and make clear the US has the "unquestionable ability to defend itself".
As Mr Tillerson downplayed Mr Trump's remarks, the President flexed his muscles further by boasting the US' nuclear arsenal was "more powerful than ever".
He added: "Hopefully we will never have to use this power, but there will never be a time that we are not the most powerful nation in the world!"
@realDonaldTrumpMy first order as President was to renovate and modernize our nuclear arsenal. It is now far stronger and more powerful than ever before....12:56 PM - Aug 9, 201716,842 11,348 40,937 Donald J. Trump
...Hopefully we will never have to use this power, but there will never be a time that we are not the most powerful nation in the world!Earlier on Tuesday, the Washington Post reported that North Korea has successfully made a miniaturised nuclear warhead that can fit inside one of its intercontinental ballistic missiles.1:03 PM - Aug 9, 201715,360 12,592 47,355 Donald J. Trump
|Trump: N Korea 'best not make any more threats'|
An analyst who specialises in North Korea, who asked not to be named, told Sky News he believes Pyongyang is "a lot more than halfway" to achieving its aims of producing a nuclear weapon capable of exploding above the US mainland.
He added: "It's fair to say it's just a matter of time, in terms of being able to hit the hit the US with a (nuclear) missile."
|Guam, a US territory in the western Pacific Ocean, is home to more than 160,000 people|
On Monday, North Korea responded angrily after the UN imposed tough new sanctions on the isolated state following the test-firing of intercontinental ballistic missiles.
Pyongyang said the sanctions were caused by a "heinous US plot to isolate and stifle" the country - and its officials also threatened to make America "pay the price for its crime... thousands of times".