WASHINGTON • United States President Donald Trump said he has received another "beautiful letter" from Mr Kim Jong Un and expressed openness to holding a third summit with the North Korean leader.

Indicating that he continues to trust Mr Kim, despite making little progress in efforts to get Pyongyang to give up its nuclear weapons, Mr Trump said the North Korean strongman "has kept his word".

"That's very important to me," he said at the White House on Tuesday.

Mr Trump did not divulge what was in the letter from Mr Kim.

He has described previous letters as "beautiful" and even said that he and the leader of one of the world's most repressive countries "fell in love".

North Korea's state media has not mentioned any letter this time.

Mr Trump has made history by meeting twice with Mr Kim in a bid to lure North Korea into giving up its nuclear weapons. But US intelligence officials say Pyongyang has no intention of following through.

In June last year, Mr Trump and Mr Kim agreed at the first US-North Korea summit in Singapore to work towards the complete denuclearisation of the Korean peninsula, easing fears of war between their countries.

But the optimism all but evaporated in February this year when a second summit, in Vietnamese capital Hanoi, dramatically fell apart without even a re-commitment to the general goals outlined in Singapore.

In the weeks leading up to yesterday's anniversary of the Singapore summit, North Korean state media repeatedly warned that the statement signed in Singapore was in danger of being rendered meaningless if the US did not drop demands for North Korea to unilaterally dismantle its nuclear arsenal.

Despite widespread perception that the Hanoi summit was a failure, Mr Trump said he would be open to an eventual third meeting.

"It could happen but I want to bring it further down the line," said Mr Trump.