US president is keen for a fourth meeting with North Korean leader Kim Jong-un, but has little to show from the previous three encounters

Donald Trump’s unshakeable belief in his ability as a peacemaker has raised the prospect of another attempt to solve one of the world’s most implacable crises: North Korea’s continuing development of nuclear weapons.

During an occasionally fractious meeting with Lee Jae Myung in the White House on Monday, Trump did at least agree with South Korea’s liberal president on the need to engage with the North’s leader, Kim Jong-un.

“Someday I’ll see him. I look forward to seeing him. He was very good with me,” Trump told reporters, adding that he hoped talks could happen before the end of the year.

If it happens, it would be the fourth time Trump has met the North Korean leader, with whom he has forged a close and potentially pivotal relationship. However, hopes for a breakthrough with a man Trump once derided as “little rocket man” appear to be as dim as ever.