Donald Trump, the US president, has praised Kim Jong-un for being “very open and terrific” and said he expects to hold a second summit with the North Korean leader “in the not too distant future.”

“I think we have done very well with regards to North Korea,” he told the press as he met with Moon Jae-in, the South Korean president, on the margins of the United Nations General Assembly in New York on Monday.

His comments were in stark contrast to his debut address at last year’s general assembly when he threatened to “totally destroy” North Korea and denounced Kim as “rocket man.” Pyongyang responded by calling the US president “mentally deranged.”

However, returning to New York for this year’s gathering, Mr Trump hailed “tremendous progress” to halt Pyongyang’s nuclear and ballistic missile tests and said that Kim “wants to see something happen.”

His positive statement followed a three-day meeting last week between the South and North Korean leaders in Pyongyang, during which Kim agreed to shut down a key missile test facility and to possibly destroy the country’s main nuclear complex in return for unspecified reciprocal US measures.

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Mr Trump’s mention of a second summit confirmed that Kim’s concessions, although minor, were enough to overcome a recent stalemate between Washington and Pyongyang over the progress of denuclearisation.

The US president held his first historic meeting with Kim Jong-un in Singapore in June but the details of their agreement over disarmament were vague, with no timeline or indication on how the steps towards denuclearisation would be achieved or verified.

In the months since the Singapore summit, talks have faltered over North Korea’s unwillingness to start dismantling its nuclear weapons programme without first having firmer security guarantees from Washington.

Speaking at the UN headquarters in New York, Mr Trump said that Mike Pompeo, the US secretary of state would arrange the next summit "in the immediate future".

“Make no mistake, the conversations that we’re having now are important. They’re putting the opportunity to complete the denuclearisation in place,” Mr Pompeo told reporters.

Moon Jae-in and Kim Jong-un travelled to the top of Mount Paektu during a three-day summit last week credit: KCNA via KNS /AFP

But analysts have pointed out that little concrete change has occurred so far beyond North Korea suspending its missile testing, and that a second summit will increase pressure on the US president to pin Kim down on specifics.

Pyongyang has not yet met US demands to provide an inventory of its nuclear arsenal or allowed weapons inspectors into the country. There have been indications that North Korea is still making fissile material for nuclear bombs.

In her first public comments since taking over the reins as CIA chief, Gina Haspel indicated that it would be a tough task to persuade the North Koreans to give up their nuclear weapons.

“They have stated that they believe it is essential to their regime’s survival, so I believe that the North Koreans view their capability as leverage and I don’t think that they want to give it up easily.”

Haspel said, however, that she believes the U.S. is in a better place than during North Korea's unprecedented level of testing last year "because of the dialogue we've established between our two leaders."