"I just got a great letter from Kim Jong Un," Trump told a cabinet meeting, reiterating that he still expected to hold a second summit with the North Korean leader, after the pair signed a pledge on denuclearization of the Korean peninsula in Singapore last June.

"We really established a very good relationship," Trump said. "We'll probably have another meeting."

Trump has cast his first summit with Kim as a major diplomatic victory, and on Wednesday repeated his claim that there would be a "big fat war in Asia" had they not sat down to talk.

But progress has stalled since the Singapore summit with the two sides disagreeing over the meaning of their vaguely-worded declaration, and the pace of US-North Korean negotiations has slowed, with meetings and visits cancelled at short notice.

Speculation about a second Trump-Kim summit has meanwhile ebbed and flowed, with the US president saying that he hoped it would take place early this year.

In a brief tweet on Tuesday, Trump said he "look(s) forward to meeting with Chairman Kim who realizes so well that North Korea possesses great economic potential!"

The North is demanding relief from multiple sanctions imposed over its banned nuclear weapons and ballistic missile programs, and has condemned US insistence on its nuclear disarmament as "gangster-like."

In his New Year speech Kim called for the sanctions to be eased, saying that the North had declared "we would neither make and test nuclear weapons any longer nor use and proliferate them," and urged the US to take "corresponding practical actions."

Culminating in late 2017, the North has carried out six atomic blasts and launched rockets capable of reaching the entire US mainland, but has now carried out no such tests for more than a year.