US Secretary of State Mike Pompeo voiced hope that North Korean leader and President Donald Trump will meet again "in the coming months" and make significant headway on ending Pyongyang's nuclear program.

In an interview broadcast Monday, the top US diplomat cautioned it was difficult to know the timing of a third US-North Korea summit but said: "It's in America's best interest to resolve this as quickly as we can."

"I would hope in the coming months our two leaders will be back together ... in a way that we can achieve a substantive first step or a substantive big step along the path to denuclearisation," he told radio station WHP 580 in Pennsylvania's capital Harrisburg.

"Then the final, fully denuclearised North Korean peninsula can be realised, at which time, as President Trump said, there'll be a brighter future for the North Korean people. It's just hard to know what the timing will be," he said.

Trump and Kim met for the first time in June 2018, a landmark first summit between the two countries that never formally ended the 1950-53 Korean War.

A follow-up summit in February in Hanoi abruptly ended early, with Trump heeding his aides and refusing to lift sanctions until North Korea takes significant steps to denuclearise.

Trump, however, has said that he still is fond of North Korea's authoritarian young leader and recently intervened to stop the imposition of tighter US sanctions.

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