America’s top diplomat left North Korea on Saturday after two days of negotiations, saying much remained to be done but insisting the two sides had discussed the idea of Pyongyang making a full declaration of its weapons of mass destruction stockpiles and setting a timeline for giving them up.

“These are complicated issues but we made progress on almost all of the central issues,’’ Mr Pompeo told reporters on the airport tarmac before leaving Pyongyang, following his third visit to North Korea. According to Bloomberg News, he added: “We had productive, good-faith negotiations.”

But just hours later, North Korea said the talks with the US delegation had been regrettable, and it accused Washington of trying to unilaterally pressure the country into abandoning its nuclear arsenal. An official said the US's behaviour was "gangster-like".

Trump says media coverage of his North Korea summit 'almost treasonous'

The statement by an unnamed foreign ministry spokesman came hours after Mr Pompeo concluded the discussions with North Korean officials led by Kim Yong-chol. They were the first formal follow-up to the meeting Donald Trump held with Kim Jong-un in Singapore on 12 June.

The statement said the US had betrayed the spirit of last month’s summit between Mr Trump and Mr Kim, by making unilateral demands on “CVID”, or the complete, verifiable and irreversible denuclearisation of North Korea.

Singapore Summit: historic first meeting between Trump and Kim Jong-un Show all 20 1 /20 Singapore Summit: historic first meeting between Trump and Kim Jong-un Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim leave following their historic meeting AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim sign a document committing to peace between their nations, amongst other things EPA Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump holds up a document that both he and Mr Kim have signed AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un The two leaders reach out to shake hands for the first time AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim shake hands as they meet for the first time Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim walk off stage, following their historic meeting Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim take a stroll after their meeting on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim interrupt their stroll to talk to the media AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Kim and Mr Trump look out over a balcony at the Capella hotel, where they held their meeting on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump takes questions at the press conference following his meeting with with Mr Kim AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump appreciates the crowd in the press conference following his meeting with Mr Kim Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump travels to the Istana ahead of the summit with Kim Jong Un on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Kim Jong Un travels to the Istana ahead of the summit with President Trump on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Kim poses for a photo with Singapore's Finance Minister Vivian Balkrishnan and Education Minister Ong Ye Kung ahead of the summit with Mr Trump Twitter/Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump shakes hands with Singapore Prime Minister Lee Hsien Loong, meeting on Monday June 11 in the Istana, Singapore's presidential palace AP Singapore Summit: historic first meeting between Trump and Kim Jong-un At a working lunch on Monday, Singapore's Prime Minister surprised Mr Trump with a birthday cake, in early celebration of his 72nd birthday later in the week EPA Singapore Summit: historic first meeting between Trump and Kim Jong-un US Secretary of State Mike Pompeo answers questions about the summit at a press briefing in Singapore on Monday, June 11 Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un US President Donald Trump arrives at the Paya Lebar Air Base in Singapore on June 10, two days prior to his summit with North Korean leader Kim Jong Un Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim met on Tuesday June 12 in the Capella hotel on the island resort of Sentosa, just off the south coast of Singapore AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump boards Air Force One following the summit AFP/Getty

It said the outcome of the follow-up talks was “very concerning” because it had led to a “dangerous phase that might rattle our willingness for denuclearisation that had been firm”.

South Korea’s Yonhap news agency said the North Korean comments had been made by an unnamed foreign ministry spokesman and carried by the Korean Central News Agency.

“We expected that the US side would come with productive measures conducive to building trust in line with the spirit of the North-US summit and [we] considered providing something that would correspond to them,” the North Korean spokesman said.

“The US just came out with such unilateral and robber-like denuclearisation demands as CVID, declaration and verification that go against the spirit of the North-US summit meeting.”

Calling the talks “really disappointing”, the spokesman rejected what it described as a US demand for unilateral action by North Korea and reiterated Pyongyang’s call for a “phased” and “synchronous” approach.

“It would be the shortest path towards realisation of the denuclearisation of the Korean peninsula to ... boldly break away from the failure-ridden methods of the past, push for whole new approaches and seek to resolve problems one by one based on trust and in a phased and synchronous principle,” he said.

While Mr Pompeo, who did not meet with the country’s top leader on this trip, could not point to any concrete agreements from the talks, he said the two sides had agreed to meet again on 12 July in Panmunjom, the border village between the two Koreas, to discuss returning the remains of US soldiers from the 1950-53 Korean War.

“I think we made progress in every element of our discussions,“ he said, according to a pool report from US reporters who accompanied him.

“These are complicated issues but we made progress on almost all of the central issues. Some places a great deal of progress, other places there’s still more work to be done.”

Before leaving North Korea for Tokyo, Mr Pompeo shook hands with his interlocutor, Mr Kim, a top North Korean party official and former spy agency chief, with whom he played a key role in arranging an unprecedented meeting between Mr Trump and the North Korean leader in Singapore on 12 June.

“We will produce an outcome, results,” Mr Kim told Mr Pompeo via a translator, according to the pool report.

Asked about reports based on US intelligence assessments that North Korea had continued to develop its nuclear facilities even while engaging in dialogue, Mr Pompeo said: “We talked about what the North Koreans are continuing to do and how it’s the case that we can get our arms around achieving what Chairman Kim and President Trump both agreed to, which is the complete denuclearisation of North Korea.”

He added: “There is no one who walked away from that, they’re still equally committed, Chairman Kim is ... still committed.”

Before the US launched its detente with North Korea after 70 years of hostilities, a number of experts warned that the country would not simply roll over and give up its nuclear weapons. Reuters reported that some officials in the US State and Defence departments and in US intelligence agencies are worried Mr Trump has put himself at a disadvantage by overstating the results of the Singapore summit on 12 June.

Mr Pompeo had said before Singapore that Trump would reject anything short of “complete, verifiable and irreversible denuclearisation”.

Part of the problem may be the mixed messages being sent by the US.

Last week, Mr Trump’s hawkish national security advisor John Bolton said the US could dismantle North Korea’s nuclear and ballistic missile programmes within a year if the North Koreans committed to scrapping their arsenal in accordance with the agreement reached in Singapore last month.

“We’re very well aware of North Korea’s pattern of behaviour over decades of negotiating with the United States,” he told CBS.

“We know exactly what the risks are of them using negotiations to drag out the length of time they have to continue their nuclear, chemical, biological weapons programmes and ballistic missiles.”

On the same day, Mr Trump told Fox News it was possible the talks could “fall apart”. Yet days later, talking to supporters in Montana, he insisted he said of the thin, detail-light agreement he signed with Mr Kim: “We signed a wonderful paper saying they’re going to denuclearise their whole thing. It’s going to all happen.”

Reports said that Mr Pompeo, who left North Korea for talks in Japan on Saturday, had spoken with Mr Trump, Mr Bolton and White House chief of staff John Kelly by secure phone before starting Saturday’s second session of talks.

Talking in front of reporters, North Korean negotiator Mr Kim had asked Mr Pompeo if he had slept well. He said he had.

“There are things that I have to clarify,” Mr Kim said. Mr Pompeo responded: “There are things that I have to clarify as well.”