The United States (US) wants a diplomatic solution to the North Korean nuclear crisis, Defense Secretary Jim Mattis said on Tuesday, as China warned there would be “no winners” in a war on the Korean peninsula.

Tensions have soared after Pyongyang claimed the US had declared war against it, and threatened to shoot down US bombers, in an escalating spat between President Donald Trump and the isolated regime.

After the White House took the unusual step of denying it had opened the door to conflict with the nuclear-armed Asian nation, Mattis said Washington's goal was “to solve this diplomatically”.

“We maintain the capability to deter North Korea's most dangerous threats but also to back up our diplomats in a manner that keeps this as long as possible in the diplomatic realm,” he said in New Delhi after talks with his Indian counterpart.

The Pentagon chief's emphasis on diplomacy comes as Trump and North Korean leader Kim Jong-Un traded barbs in the wake of the North's sixth nuclear bomb and multiple missile tests. Pyongyang says it needs the weapons to defend itself against the threat of a US invasion.

The North's Foreign Minister Ri Yong-ho on Monday called a press conference to hit back at a US bomber mission near the North's coastline and a slew of bombastic warnings from the American president.

Taking umbrage at Trump's weekend tweet that North Korea's leadership “won't be around much longer” if it keeps up its threats, Ri told reporters that the international community 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,” said Ri, who attended this year's United Nations (UN) General Assembly session.

“He declared a war on our country.”

The White House said Ri's interpretation of Trump's sabre-rattling as “absurd”.

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

China, the North's neighbour and only major ally, warned on Tuesday that any conflict would have “no winners”.

Chinese Foreign Ministry Spokesman Lu Kang told a regular briefing that the rhetorical sparring “will only increase the risk of confrontation and reduce the room for policy manoeuvres”.

South Korean President Moon Jae-in cautioned that the security situation on the peninsular was now “more serious than ever”, according to the Yonhap news agency.

“We will make North Korea realise that it has no future should it try to face the rest of the world with nukes,” he said, though he added there was still a chance for dialogue.

Fears of a clash were sharpened after US bombers flew off the coast of North Korea on Saturday, going further north of the demilitarised zone than 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 the bombers flew in international airspace and had every right to do so.

South Korea's National Intelligence Service (NIS) said that while Pyongyang did not appear to have picked up the presence of the US warplanes over the weekend, it had since bolstered 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 tensions reached fever-pitch, there have been repeated appeals for calm from the UN, Russia and China.

South Korea, whose densely-populated capital Seoul is located just 35 miles from the demilitarised zone dividing the Korean peninsula, has also asked the US to take the heat out of the situation.

South Korean Foreign Minister Kang Kyung-wha in Washington said it was imperative to “prevent further escalation of tensions or any kind of accidental military clashes which can quickly go out of control”.

In his UN address last week, Trump delivered the blunt threat to “totally destroy” North Korea if provoked, deriding leader Kim Jong-un as “Rocket Man”.

Kim hit back with a personal attack, branding Trump “mentally deranged” and a “dotard” and warning he would “pay dearly”.

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”.