Donald Trump said he is expecting a second meeting with North Korean leader Kim Jong-un “pretty soon”, but that is unlikely to take place in Singapore, location of their first summit this summer.

The president, while in a meeting with South Korean President Moon Jae-in during the United Nations General Assembly in New York, said "Chairman Kim has been really very open and terrific, frankly. I think he wants to see something happen".

Mr Moon also said he brought a personal message to Mr Trump from the North Korean leader, with whom he met and signed another peace agreement last week.

Mr Trump said secretary of state Mike Pompeo would make the arrangements for the second meeting with Mr Kim “in the immediate future”.

The first summit between the pair took place on 12 June in Singapore and White House press secretary Sarah Huckabee Sanders had confirmed the receipt of a letter requesting the meeting from Mr Kim on 10 September.

She described it as “warm” and “positive”, but said the letter would not be released to the public in full.

There has been “tremendous progress” in improving relations between the isolated regime in Pyongyang and Washington, the US president said.

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

A year ago, at the 2017 General Assembly, Mr Trump stood at the podium for his first speech at the UN and called Mr Kim “rocket man” and threatened a military strike if North Korea did not take steps to halt the development and testing of nuclear weapons.

"That was a very dangerous time. This is one year later, a much different time,” the US president said.

Pyongyang launched a test missile as late as November 2017.

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However, tensions appeared to thaw with the Winter Olympics in Pyeongchang, South Korea, this past February.

The two Koreas not only marched together in the opening and closing ceremonies, competed as a unified team in ice hockey, but Mr Kim sent his sister Kim Yo Jong as an emissary.

After receipt of the most recent letter, Ms Sanders pointed to a recent military parade held in Pyongyang as a “sign of good faith” in the denuclearisation talks because it did not feature any long-range missiles as Mr Kim has had before, adding it was “a continued commitment to focus on denuclearisation of the peninsula”.

Perhaps another sign of progress is the recent trade and peace agreement signed by Mr Moon and Mr Kim.

At a signing ceremony, the pair raised their arms, holding hands as a sign of a “leap forward” towards a “land of peace”, as Mr Kim had described it.

He added: "The world is going to see how this divided nation is going to bring about a new future on its own."