Donald Trump has declared that the US is "totally prepared" to take a military option against North Korea, saying "it will be devastating" to Pyongyang.

The US president was reacting to reports of a North Korean threat to shoot down American bombers, after what the country called a declaration of war.

"We are totally prepared for the second option. Not a prefered option. But if we take that option it will be devastating, I can tell you that, devastating for North Korea," Trump said on Tuesday from the White House.

"That's called a military option. If we have to take it, we will."

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Earlier, the US dismissed North Korea's accusation that Trump has declared war as "absurd".

The heated exchange came as South Korea's National Intelligence Service (NIS) said Pyongyang had moved to bolster its coastal defences by relocating its warplanes along the east coast.

Regional leaders on Tuesday warned that war on the Korean Peninsula would result in "catastrophic consequences".

Trump also said that the North Korea problem could have been dealt with in the past, blaming "past administrations" for not taking action.

"North Korea should have been handled 25 years ago, 20 years ago, 15 years ago, 10 years ago, five years ago, and it could have been handled more easily," he said.

"You have various administations, which left me a mess. But I'll fix the mess. So we will see what happens with North Korea."

On Monday, Ri Yong-ho, North Korea's foreign minister, said recent comments by Trump means a war declaration.

"Last weekend, Trump claimed our leadership would not be around much longer," Ri said. "He declared a war on our country."

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Alarm over Pyongyang's nuclear and ballistic missile programmes dominated this year's gathering of world leaders at the UN General Assembly, amid fears the heated rhetoric could accidentally trigger a war.

Those fears were sharpened after US bombers flew off the coast of North Korea on Saturday - going the furthest north of the demilitarised zone that any US aircraft has flown this century.

"Since the United States declared war on our country, we will have every right to take counter-measures including the right to shoot down US strategic bombers even when they are not yet inside the airspace border of our country," Ri said.

"The question of who won't be around much longer will be answered then."

A Pentagon spokesman stressed on Monday that the bombers flew in international airspace and had every right to do so.

As the rhetoric heated up, South Korea appealed for an easing of tensions, with Foreign Minister Kang Kyung-wha saying that further provocations can be expected from Pyongyang but must not be allowed to get out of control.

"It is imperative that we, Korea and the US together, manage the situation ... in order to prevent further escalation of tensions or any kind of accidental military clashes which can quickly go out of control," Kang said in Washington.

South Korea has reacted with unease to Trump's threat to "totally destroy" North Korea as its densely-populated capital Seoul is located just 56 kilometres from the demilitarised zone dividing the Korean Peninsula.

In his UN address last week, Trump delivered the blunt threat, deriding leader Kim Jong-un as "Rocket Man" and declaring he was "on a suicide mission".

Kim hit back with a personal attack on Trump, branding him "mentally deranged" and a "dotard" and warning he would "pay dearly" for his threat.

There have been repeated appeals for calm from the United Nations, Russia and China.

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On Tuesday, China said that war on the Korean Peninsula will have no winner.

Lu Kang, the spokesman for the Chinese foreign ministry, said Beijing hopes that US and North Korean politicians can realise that resorting to military means would never be a viable way out.

Russia's foreign ministry also said on Tuesday that a military conflict on the Korean Peninsula would lead to "catastrophic consequences".

It added that it would work behind-the-scenes to find a political solution to the rising tensions with North Korea, and that the US approach is a "dead in".