Washington: US President Donald Trump has said that he has received a "great letter" from Kim Jong-un and is looking forward to meet the North Korean leader for a second time in the "not-too-distant future" to restart talks about the denuclearisation of the Korean Peninsula.

President Trump's announcement came after the North Korean leader warned that Pyongyang may change its approach to nuclear talks if Washington persists with sanctions.

"I just got a great letter from Kim Jong-un. Those few people that I've shown this letter to, they've never written letters like that. This letter is a great letter. We've made a lot of progress with North Korea and Kim Jong-un," Trump told his Cabinet colleagues during a meeting on Wednesday.

"North Korea has tremendous economic potential and so I look forward to our meeting with Chairman Kim. We'll set that up. We'll be setting it up in the not-too-distant future," he said.

Trump said he and Kim had established a very good relationship.

"A lot of good things are happening. I never said speed. Look, it's been this way for 80 plus years," he said.

Kim and Trump held a historic meeting in Singapore on June 12 last year. They issued a vague goal for the "complete denuclearisation" of the Korean Peninsula without describing when and how it would occur.

"We'll probably now have another meeting. He'd like to meet, I'd like to meet, but we've established a very good relationship," he said.

Trump said his administration was not getting any credit for this peace initiative which has averted the world from a major war.

"We're given no credit for frankly if this administration didn't take place, if another administration came in instead of this administration, namely (Vice President) Mike (Pence) and myself and the group around this table, you'd be at war right now," he said.

"You'd be having a nice big, fat war in Asia and it wouldn't be pleasant," he added.

Trump said he was in no rush for the denuclearisation of the Korean peninsula.

"We're getting along fine. I'm not in any rush. I don't have to rush. All I know is there's no rockets, there's no testing," he said, expressing satisfaction over the progress in talks with the North Koreans.

North Korea really want to do something, he said.

"Now, does that mean it's going to be done? Who knows? Who knows? Deals are deals. You never know but I tell you, we've established a very good relationship with North Korea," he said.

"That was going to be a war, that could have been a World War III to be honest with you because a lot of people would've had to get involved in that all over Asia and then it spreads beyond Asia, and instead we have somebody that I really think wants to get onto economic development and making a lot of success and money, frankly, for his country because North Korea has tremendous potential and will help them out," Trump said.