Trump said at the White House that the meeting would "probably" not be in Singapore, where their historic first talks took place in June.

The pair discussed ending the reclusive state's nuclear weapons program and hostilities between Washington and Pyongyang.

Trump said that in terms of timing, the summit "won't be that far away."

He also said that "eventually" there could be a meeting on US soil.

"On their soil also," he added.

US Secretary of State Mike Pompeo met with Kim on Monday in Pyongyang to discuss a future summit and told reporters the North had made "significant progress" toward denuclearization.

He said international inspectors would be allowed into the country to inspect a nuclear test site that Pyongyang has said it dismantled.

"I think we've made incredible progress," Trump said Tuesday, hailing the absence of missile or nuclear tests this year and the recent return of remains of US service members killed during the Korean War.

"No nuclear tests, no rockets, and we have a very good relationship with Chairman Kim, which is very important," Trump said.

"I like him, he likes me, the relationship is good."