A spokesman for the Korean People's Army, in a statement carried by the North's state-run KCNA news agency, said the strike plan will be "put into practice in a multi-current and consecutive way any moment" once leader Kim Jong-un makes a decision.
In another statement citing a different military spokesman, North Korea also said it could carry out a pre-emptive operation if the US showed signs of provocation.
Trump threatened North Korea "with fire and fury like the world has never seen" on Tuesday after reports suggested the communist country has mastered one of the final hurdles to being able to strike the US with a nuclear missile.
The nuclear advances were detailed in an official Japanese assessment and a Washington Post story that cited US intelligence officials and a confidential Defense Intelligence Agency report. The US now puts the North Korean arsenal at up to 60 nuclear weapons, more than double most assessments by independent experts, according to the Post's reporting.
"North Korea had best not make any more threats to the United States," said a stern-looking Trump, seated with his arms crossed and with his wife beside him, at his golf course in Bedminster, New Jersey. "They will be met with fire and fury like the world has never seen." The remarks appeared scripted, with Trump glancing at a paper in front of him. They evoked President Harry Truman's announcement of the US atomic bomb dropped on Hiroshima, Japan, in 1945, in which he warned of "a rain of ruin from the air, the like of which has never been seen on this earth".
Al Jazeera's Heidi Zhou-Castro, reporting from Washington DC, said that the missile that North Korea is threatening to hit Guam with was tested in May and South Korea's intelligence analysts concluded it was capable of flying up to 5,000 kilometres, "which does make Guam well within striking range".
Guam hosts strategic US military installations - including both a naval and an air force base - and is more than 3,400km from North Korea. It's population is around 160,000 - but only about 6,000 US troops are currently stationed there.
Robert Kelly, professor of political science at Pusan National University, told Al Jazeera that both North Korea and Trump were almost certainly exaggerating in their respective rhetoric, as a conflict would be disastrous - and that Trump was likely stepping up the rhetoric to pressure China into taking action to curb North Korea's behaviour.
"If the North Koreans were to strike Guam and kill a lot of Americans it would lead to a war which would destroy North Korea, so my guess is this is bluffing on both sides," he said.
"But it certainly doesn't help because it raises the possibility of miscalculation and misperception," added Kelly.
Escalating tensionsThe Trump administration considers North Korea to be America's greatest national security threat and tensions have steadily escalated this year.
Pyongyang had threatened the US in response to the UN Security Council's adoption this weekend of new, tougher sanctions spearheaded by Washington. The sanctions followed groundbreaking long-range missile tests last month that showed the North could potentially reach the continental US with its missiles. The newly revealed US intelligence assessment indicates those missiles can carry nuclear warheads.
Denouncing the UN sanctions through state media, 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." For North Korea, having a nuclear-tipped missile that could strike America would be the ultimate guarantee against invasion by its superpower adversary.
In an annual report, Japan's Defense Ministry on Tuesday concluded that "it is possible that North Korea has achieved the miniaturisation of nuclear weapons and has developed nuclear warheads." Japan, a key US ally, is a potential, front-line target of North Korean aggression.
The Post story, citing unnamed US intelligence officials, went further. It said the Defense Intelligence Agency analysis, completed last month, assessed North Korea has produced nuclear weapons for ballistic missile delivery, including by intercontinental missiles.
Remaing hurdlesLast month's tests of intercontinental ballistic missiles highlighted the growing threat. While those missiles landed at sea near Japan, both were fired at highly lofted angles. Analysts said the weapons could reach Alaska, Los Angeles or Chicago if fired at a normal, flattened trajectory.
Not all technical hurdles have been overcome with the missiles, however. North Korea is still believed to lack expertise to allow a missile to re-enter the Earth's atmosphere without burning up. Another work-in-progress: the ability to strike targets with accuracy.
After the launches, missile expert John Schilling concluded the intercontinental missile still needed another year or two to achieve "full operational capability".
Al Jazeera's Patty Culhane, reporting from Washington DC, said the Trump administration's responses to the threat posed by North Korea have been inconsistent.
"We've seen the US Secretary of State say that he's willing to negotiate with North Korea. The US ambassador to the United nations said the time for talk is over. The CIA director hinted that the US was looking for regime change in North Korea," she said.
"On the campaign trail [Trump] said that the fact that he is unpredictable was an asset. We're about to find out in a very high stakes test if he's right."