Seoul, South Korea: US warplanes flew close to North Korea’s coast on Saturday, the same day that the North’s foreign minister told the United Nations (UN) General Assembly that President Donald Trump’s threats against the country were “making our rocket’s visit to the entire US mainland inevitable all the more”.

On Twitter, Trump responded to Foreign Minister Ri Yong-ho’s speech with yet another threat. Saying he had heard Ri’s speech, and using his recently coined nickname for the North’s leader, Kim Jong-un, Trump wrote: “If he echoes thoughts of Little Rocket Man, they won’t be around much longer!”

Earlier on Saturday, the Pentagon said the Air Force had sent B-1B bombers and F-15C fighters over waters north of the demilitarised zone separating the two Koreas, in response to what it called the North Korean government’s “reckless behaviour”. It was the farthest north “any US fighter or bomber aircraft have flown off North Korea’s coast in the 21st century”, Dana W. White, the Defence Department’s chief spokeswoman, said in a statement.

“This mission is a demonstration of US resolve and a clear message that the President has many military options to defeat any threat,” White added.

Although B-1B bombers have flown near the demilitarised zone over land several times, this flight seemed intended to underscore US military strength to Kim, who has been engaged in a war of words with Trump.

At the General Assembly on Saturday, Ri said that North Korea intended to have a “nuclear hammer of justice” against its rivals and boasted that it was “a few steps away” from becoming a nuclear power.

Referring to Trump’s threat — in his General Assembly address on Tuesday — to “totally destroy” North Korea, Ri said the US President had “committed an irreversible mistake”.

“None other than Trump himself is on a suicide mission,” he added.

But Ri also said the North’s nuclear programme was a deterrent intended to avert an invasion, with the ultimate goal being “balance of power with the US”.

“We do not have any intention at all to use or threaten to use nuclear weapons against the countries that do not join in the US military actions against” North Korea, Ri said.

Over the years, as Pyongyang raced to build a nuclear arsenal, the world has often turned to its neighbours for help: China, because of its economic leverage over the North, and South Korea, because it would suffer the most in any military confrontation.

Now, China and South Korea have been left squirming on the sidelines, with Kim having been essentially granted his wish: dealing directly with the US, which the North believes has the most to give.

To the North Koreans, the US can offer a peace treaty, diplomatic recognition, the easing of sanctions and the withdrawal of US troops from South Korea, which the North considers its existential threat.

Since Kim came to power nearly six years ago, North Korea has accelerated its nuclear and missile tests to grab Washington’s attention and to force negotiations on terms favourable to the North, according to South Korean intelligence officials and analysts who study Kim’s motives.

When Trump made his threat on Tuesday it gave Kim a perfect chance to square off directly against the US, they said. In an unprecedented personal statement on Friday, Kim called Trump a “mentally deranged US dotard”, and Ri raised the prospect of exploding a hydrogen bomb over the Pacific.

To back up such talk, Kim will probably carry out more weapons tests, analysts said.

A tremor detected on Saturday near North Korea’s underground nuclear-testing site raised fears of another detonation, but South Korean experts said it appeared to have been a natural earthquake.

“We now can’t avoid the military tensions on the Korean Peninsula further escalating,” said Cheong Seong-chang, a North Korea expert at the Sejong Institute, a think tank near Seoul, the South’s capital. The standoff is intensifying partly because, “South Korea lacks capabilities to confront North Korea while the North ignores the South and insists on dealing only with the United States”, Cheong added.

As the crisis spiralled over the last few days, China found itself a bystander — an uncomfortable role for President Xi Jinping, who was most likely seething about Kim and about the North Korean government’s criticism of China’s most vaunted institution, the Communist Party, as its leadership prepares to meet, analysts said. The North’s Korean Central News Agency referred to a coming party congress in Beijing in unflattering terms on Friday.

The quiet in Beijing illustrated China’s almost complete lack of influence in controlling the North and its unsuccessful efforts to persuade Trump to tamp down his language, they said.

Fearful of failing and of losing face in a peacemaking role, Xi would be reluctant to make any diplomatic or strategic moves before the party congress opens on October 18, analysts said.

Xi was left merely humouring Trump by agreeing to tougher sanctions at the UN this past week.

“I think China’s diplomatic leverage over North Korea is zero,” said Feng Zhang, a fellow at the Australian National University’s department of international relations. “North Korea doesn’t want to see Chinese envoys and is not interested in Chinese views.”

President Moon Jae-in of South Korea has also found room for diplomacy shrinking, as North Korea and the US locked themselves in what he called an escalating “vicious cycle” of provocations and sanctions.

North Korea has not responded to Moon’s calls for dialogue as it accelerates its missile and nuclear tests. When he came to power in May, Moon found little leverage left over North Korea: Under his conservative predecessors, South Korea had cut off all trade ties and pulled out all investments in North Korea.

“We need a breathing room, an easing of tensions,” Moon said on Friday.