Video report by ITV News Correspondent Juliet Bremner
North Korea says it will finalise a plan for striking waters close to Guam with mid-range missiles by mid-August.
State media reported that the plan would involve the missiles hitting waters 30 to 40 kilometres away from the US Pacific territory and Kim Jong-Un will decide whether to proceed.
The statement published through the Korean Central News Agency (KCNA) also officially dismissed President Donald Trump's warnings of "fire and fury," on North Korea if it issues any more threats.
KCNA quoted Kim Jong-Un as saying: "Sound dialogue is not possible with such a guy bereft of reason and only absolute force can work on him".
Kim said the Guam action would be "an effective remedy for restraining the frantic moves of the US in the southern part of the Korean peninsula and its vicinity."
He called Trump's rhetoric a "load of nonsense" that was aggravating a grave situation.
The long-standing tensions between the nations have escalated after both performed missile tests and new UN sanctions were imposed against North Korea at the weekend.
Japan and South Korea vowed a strong reaction if the North were to go through with the plan.
Japan's defence minister Itsunori Onodera told parliament a missile attack on the US territory would be a Japanese national emergency because it would threaten Japan's existence as a nation.
First Secretary of State Damian Green said it is "obviously" in Britain's interests that the stand-off between Washington and Pyongyang does not lead to conflict.
He said the "sensible" way to proceed is to step up international pressure on the regime of Kim Jong Un through the United Nations.
Why would North Korea strike Guam?
North Korea sees Guam, which houses America's Andersen Air Force Base, as a launchpad for a potential US invasion.
It is considering firing medium to long-range ballistic missiles to create an "enveloping fire" to contain US air bases on the island, which lies around 1,500 miles south of Tokyo in the Pacific Ocean.
The North Korean army said it is examining operational plans for attacking Guam with its Hwasong-12 missiles, which it says can carry a heavy nuclear warhead.
The statement said the move is in response to a recent US test of an ICBM (inter-continental ballistic missile).
Is the threat credible?
A nuclear expert who has repeatedly visited North Korea's nuclear facilities says he doubts the country is yet capable of such a strike.
Professor Siegfried Hecker of Stanford University said although the North tested two intercontinental ballistic missiles last month, developing a nuclear warhead for such a missile is "extremely challenging and still beyond North Korea's reach".
But he said the escalating rhetoric was the bigger danger.
The real threat is "stumbling into an inadvertent nuclear war on the Korean Peninsula by misunderstanding or miscalculation," he said, adding: "Inflammatory rhetoric on both sides will make that more likely."
What is the response in Guam to North Korea's statement?
Guam's security and defence officials say there is no imminent threat to its 160,000 population or in the neighbouring Northern Mariana Islands.
Governor Eddie Baza Calvo though said discussions were underway to have its military "prepared for any eventuality".
Guam politician Madeleine Z. Bordallo said Pentagon officials had assured her the territory is protected.
She also condemned President Trump's "fire and fury" threat as unnecessarily provocative and called on him to work with the international community to de-escalate tensions.
What exactly did Trump say?
ITV News Correspondent Juliet Bremner on Trump's warning
The US president made the extraordinary blunt warning after reports of significant advances in North Korea's nuclear programme.
The leaked document from late July, reported by the Washington Post, said: "The IC (intelligence community) assesses North Korea has produced nuclear weapons for ballistic missile delivery, to include delivery by ICBM (inter-continental ballistic missile)."
The US president was questioned about it during a photo call at the Trump National Golf Club in Bedminster, New Jersey.
Sat at a table with crossed arms, Mr Trump said: "North Korea best not make any more threats to the United States.
"They will be met with fire and fury like the world has never seen... (Kim Jong-Un) has been very threatening beyond a normal state.
"They will be met with fire, fury and frankly power the likes of which this world has never seen before."
Secretary of Defence Jim Mattis also warned North Korea against pursuing a policy which led to "the end of its regime and the destruction of its people".
Why has he faced criticism for the comments?
ITV News China Correspondent Debi Edward provides analysis
The colourful threat is seen as exactly the sort of provocation that escalates tensions with North Korea.
China has pressed for calmer language rather than an echoing of the sort of hyperbolic threats Pyongyang has issued.
Republican Senator John McCain, a notable critic of the US president and chairman of the Senate Armed Services, said the comments were "classic Trump" and ill-advised given it is a threat he may not be able to carry out.
"You got to be sure you can do what you say you're going to do," he said, adding "great leaders" do not threaten foes unless they are ready to act.
Senior Democrats meanwhile condemned Mr Trump's comments as "bombastic", "reckless" and "drawing an absurd red line".
Why have tensions escalated so much?
The angry exchanges between Washington and Pyongyang have been driven by North Korea's numerous missile tests, including one said to be capable of hitting the US mainland, and expansion of its weaponry.
For North Korea, having a nuclear-tipped missile that could strike America would be the ultimate guarantee against invasion by its superpower adversary and is an ambition decades in the making.
The Washington Post said the US now estimates the North Korean arsenal is up to 60 nuclear weapons - more than double most assessments by independent experts.
The US has also carried out an intercontinental ballistic missile test in response to the provocative Pyongyang displays, while imposing new UN sanctions against North Korea.
Condemning the UN sanctions, the North warned: "We will make the US pay by a thousand-fold for all the heinous crimes it commits against the state and people of this country."