In his first public comments since leaving the White House, John Bolton, the former US national security adviser, delivered a stark warning about Donald Trump’s approach to North Korea, undercutting the president’s insistence that its leader, Kim Jong-un, wanted to make a denuclearisation deal with him.

Without mentioning Mr Trump by name, Mr Bolton said he wanted to “speak in unvarnished terms about the threat posed by North Korea,” and made it clear he thought the US president’s outreach to Mr Kim had benefited only one side.

While Mr Trump has made a deal with Mr Kim one of his signature foreign policy goals, Mr Bolton asserted there had been no gains with his approach.

“The strategic decision Kim Jong-un is operating through is that he will do whatever he can to keep a deliverable nuclear weapons capability and to develop and enhance it further,” Mr Bolton said during an appearance at the Centre for Strategic and International Studies on Monday.

“Under current circumstances, he will never give up the nuclear weapons voluntarily.”

Trump and Kim: leaders arrive in Vietnam for talks Show all 7 1 /7 Trump and Kim: leaders arrive in Vietnam for talks Trump and Kim: leaders arrive in Vietnam for talks Donald Trump and Vietnamese President Nguyen Phu Trong make their way to a meeting at the Presidential Palace in Hanoi Reuters Trump and Kim: leaders arrive in Vietnam for talks Donald Trump waves a Vietnamese flag as Vietnam's Prime Minister Nguyen Xuan Phuc looks on AFP/Getty Trump and Kim: leaders arrive in Vietnam for talks Donald Trump waves as he leaves the Presidential Palace in Hanoi AFP/Getty Trump and Kim: leaders arrive in Vietnam for talks North Korean leader Kim Jong-un, right, is welcomed on his arrival at the Melia Hotel in Hanoi AP Trump and Kim: leaders arrive in Vietnam for talks Kim Jong-un waves as he arrives by train in the Vietnamese border town of Dong Dang AP Trump and Kim: leaders arrive in Vietnam for talks North Korean leader Kim Jong-un receiving a situation report before the summit with Trump AFP/Getty Trump and Kim: leaders arrive in Vietnam for talks The motorcade carrying U.S President Donald Trump drives past Ho Chi Minh Mausoleum AP

Mr Bolton was pushed out from his job as Mr Trump’s third national security adviser less than a month ago amid disputes over how to handle major foreign policy challenges, including North Korea.

Stopping nuclear proliferation in the Korean Peninsula is where the US needs “to focus our attention,” Mr Bolton said, “not can we get another summit with Kim Jong-un or what the state of staff-level negotiations are to achieve a commitment from North Korea it will never honour”.

For Mr Trump, the showy summits have been among his signature foreign policy achievements, held up as historic firsts.

But there has been no sign that North Korea’s nuclear provocations have diminished since Mr Trump’s outreach and the exchange of “beautiful” letters from Mr Kim the president likes to show off.

Mr Trump last met with Mr Kim in June, when he crossed the Demilitarized Zone from South Korea and became the first sitting American president to set foot in North Korea.

The president delighted in the drama of the meeting and the historic handshake with the North Korean leader, which he had arranged with a surprise invitation via Twitter barely 24 hours earlier.

Mr Bolton had accompanied the president to a meeting with Mr Kim in Hanoi, Vietnam, earlier in the year, but he was on a previously scheduled trip to Mongolia when Mr Trump crossed the DMZ.

Since then, there has been little progress in terms of denuclearisation and Mr Trump has spent less time bragging about his cosy relationship with the North Korean leader.

Mr Bolton spoke on the day that was North Korea’s turn to address the annual session of the UN General Assembly.

Kim Song, the North’s ambassador to the world body, made it clear deep differences remained with the US and he suggested his government was losing patience.

Relations between the Trump administration and North Korea, the ambassador said, “have made little progress so far and the situation on the Korean Peninsula has not come out of the vicious cycle of increased tension, which is entirely attributable to the political and military provocations perpetrated by the US”.

The president has blamed Mr Bolton more than Mr Kim for the stalled talks.

“[Mr Kim] wanted nothing to do with John Bolton,” Mr Trump told reporters in September.

But Mr Bolton’s departure from the administration was expected to help revive the talks, even if it remained unclear what further concessions the North Koreans would be willing to make.

Trump becomes first sitting US president to set foot in North Korea at meeting with Kim Jong-un

“The chances of a fourth summit go up a great deal now that he’s not there,” said Victor Cha, the Korea chairman at the Centre for Strategic and International Studies.

“I don’t think there’s anybody now at his level that will show the same degree of caution and scepticism of North Korea’s intentions.”

Mr Cha said the danger was the “lifting of some of these core sanctions against North Korea in return for something that is faux denuclearisation,” in other words, an agreement to dismantle pieces of the country’s nuclear programme it does not need anymore.

At the UN General Assembly session last week, Mr Trump floated the idea another summit was in the works. “It could happen soon,” he told reporters. “It could happen soon.”

“The relationship has been very good,” Mr Trump said last week. “We’ll see what happens. But we’d like to see if we can do something. And if we can, that would be great. And if we can’t, that’s fine.”

When pressed on Monday about whether Mr Bolton thought Mr Trump’s efforts to befriend and charm Mr Kim would work, Mr Bolton demurred.

“I’m not going to comment on that,” he said. “Nice try.”

But he made clear he disagreed with Mr Trump’s position that the United States was in “no rush” for North Korea to give up its nuclear weapons.

“Time works against those who oppose nuclear proliferation,” Mr Bolton said. “A relaxed attitude to time is a benefit to the likes of North Korea and Iran.”

The differences between Mr Trump and Mr Bolton on North Korea were hardly a secret during his time at the National Security Council.

During a four-day state visit to Japan in May, Mr Trump contradicted Mr Bolton and Shinzo Abe, the Japanese prime minister, who both called North Korea’s short-range ballistic missile tests a violation of UN Security Council resolutions.

“North Korea fired off some small weapons, which disturbed some of my people, and others, but not me,” Mr Trump wrote on Twitter, noting he trusted Mr Kim to “keep his promise to me”.

Mr Trump has also cited Mr Bolton’s comments from the year before about using a “Libyan model” for disarmament in North Korea as among the reasons he was dismissed.

His reference to Muammar Gaddafi​’s agreement to swap his nascent nuclear programme for economic integration with the West angered the North Koreans who saw it as an example of why no one should trust US efforts to disarm another nation since Gaddafi was eventually killed.

Mr Bolton’s comments raised questions about what other splits with Mr Trump he may reveal. His remarks, however, were limited to North Korea.

“I was struck by how consistent his views were with what they have historically been,” said Mr Cha, who moderated a question-and-answer session with Mr Bolton on Monday.

While Mr Bolton declined to comment directly on his time in the administration, Mr Cha said “the fact that he spent all that time working on this issue, and was there in Hanoi, and he comes out and his views are still very sceptical, it speaks for itself”.