The United States dismissed as "absurd" North Korea's accusation that President Donald Trump has declared war against the regime, after Pyongyang said it was ready to defend itself by shooting down American bombers.

Speaking to reporters outside his New York hotel, Foreign Minister Ri Yong-ho responded to Trump tweeting at the weekend that North Korea's leadership "won't be around much longer" if it keeps up its threats.

Ri, who attended this year's UN General Assembly session, said the international community had hoped that a "war of words" would "not turn into real actions."

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

The White House disputed Ri's interpretation of Trump's sabre-rattling.

"We have not declared war against North Korea and frankly the suggestion of that is absurd," said White House spokeswoman Sarah Huckabee Sanders. 

Alarm over Pyongyang's nuclear and ballistic missile programmes dominated this year's gathering of world leaders at the United Nations, 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 furthest north of the demilitarized 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," said Ri.

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

South Korea's National Intelligence Service (NIS) said that while Pyongyang did not appear to have picked up the presence of the US B-1B Lancer warplanes over the weekend, it had since moved to bolster its coastal defences. 

"North Korea relocated its warplanes and strengthened defences along the east coast," said Lee Cheol-Woo, the chief of the National Assembly's intelligence committee.

- Risk of accidental clash -

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 35 miles from the demilitarized 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.

Asked about the North Korean minister's latest remarks, UN spokesman Stephane Dujarric said: "When you have the rise of tension, the rise of rhetoric, so does the risk of miscalculation."

North Korea has in recent weeks detonated its sixth nuclear bomb and test-fired intercontinental missiles -- saying it needs to defend itself against the threat of a US invasion.

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

In his UN address, Ri warned that Trump's threat to destroy North Korea made "our rockets' visit to the entire US mainland all the more inevitable".

The bellicose rhetoric comes as international alarm mounts over Pyongyang's weapons ambitions -- including a suggestion by Ri last week that the country is considering detonating an H-bomb over the Pacific.

US Defense Secretary Jim Mattis has said such a move would be a "shocking display of irresponsibility."

As tensions over North Korea reached fever-pitch, Japanese Prime Minister Shinzo Abe called a snap election, hoping to capitalize on a boost in the polls that some say is linked to his hawkish stance toward Pyongyang.

Asian financial markets sank in early trade Tuesday, as investors sought out safe havens in response to the flare-up in tensions. Gold was up more than one percent, while the Japanese yen recovered recent losses against the dollar.