The United States aspires to have North Korea as a "close partner" and not an enemy, Secretary of State Mike Pompeo said, noting the US has often in history become good friends with former adversaries.

Pompeo said he had told North Korean leader Kim Jong Un of that hope during his brief visit to Pyongyang earlier this week.

During the visit he finalised details of the June 12 summit between Kim and President Donald Trump and secured the release of three Americans imprisoned in North Korea.

He said his talks with Kim on Wednesday had been "warm", "constructive" and "good".

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He had made clear that if North Korea gets rid of its nuclear weapons in a permanent and verifiable way, the US is willing to help the impoverished nation boost its economy and living standards to levels like those in prosperous South Korea.

South Korea's visiting foreign minister, Kang Kyung Wha, praised the upcoming meeting between the two leaders in Singapore as an "historic" opportunity, but added a few notes of scepticism.

Amid concerns that North Korea will demand America withdraw its troops from neighbouring South Korea, Kang emphasised that the US military presence there must be "a matter for the US-South Korea "alliance first and foremost."

Kang said the US troop presence in the South for the past 65 years has played a "crucial role for deterrence", peace and stability on the Korean peninsula. Therefore, she said, any change in the size of the US forces in South Korea should not be on the table at the summit.

Kang said South Korean President Moon Jae In would be in Washington to see Trump later this month.

Pompeo said there would need to be complete and verifiable denuclearisation that would remove North Korea as a threat to the South, the US and the rest of the world.

He said a major inspection and monitoring regime would be required to ensure the North's compliance.

"I think there is complete agreement about what the ultimate objectives are," Pompeo said, though he declined to offer more detail.