The United States will help North Korea boost its economy and living stands to levels like those in prosperous South Korea if it gives up its nuclear weapons, Secretary of State Mike Pompeo says, adding the country aspires to have North Korea as a "close partner" and not an enemy.

Mr Pompeo said he had told North Korean leader Kim Jong-un of that hope during his brief visit to Pyongyang earlier this week, during which he finalised details of the upcoming June 12 summit between Mr Kim and President Donald Trump and secured the release of three Americans imprisoned in the country.

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He said his talks with Mr Kim had been "warm", ''constructive", and "good" and noted the US has often in history become good friends with former adversaries.

"We had good conversations about the histories of our two nations, the challenges that we have had between us," Mr Pompeo told a news conference with South Korea's visiting Foreign Minister Kang Kyung-wha.

"We talked about the fact that America has often in history had adversaries who we are now close partners with and our hope that we could achieve the same with respect to North Korea."

He did not mention other adversaries by name, but Mr Pompeo and others have often noted that the US played a major role in rebuilding Japan and the European axis powers in the wake of World War II.

With US help, those countries recovered from the devastation of conflict.

Mr Pompeo said he and Mr Kim had warm and constructive talks. ( Twitter: Sarah Sanders )

"If North Korea takes bold action to quickly denuclearise, the United States is prepared to work with North Korea to achieve prosperity on the par with our South Korean friends," he said.

Ms Kang praised the upcoming meeting between Mr Trump and Mr Kim in Singapore as an "historic" opportunity, but added a few notes of scepticism as well.

Amid concerns that North Korea will demand the US withdraw its troops from neighbouring South Korea, Ms Kang emphasised that the US military presence there must be "a matter for the US-ROK alliance first and foremost", using an acronym for South Korea's official name, the Republic of Korea.

She 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 the South Korea should not be on the table at the summit.

"The next few weeks will be critical, requiring air-tight coordination between our two countries," Ms Kang said, noting that South Korean President Moon Jae-in would be in Washington to see Mr Trump later this month.

Since Mr Trump announced plans to hold a summit with Mr Kim, questions have been raised continually about whether the two leaders have the same objective in mind when they speak about "denuclearisation".

The island-country of Singapore is friendly turf for Donald Trump. ( Flickr: Rajesh_India )

To the US, that means the North giving up the nuclear weapons it has already built. But North Korea has said it was willing to talk now because it has already succeeded in becoming a nuclear-armed state, fuelling scepticism that the North would truly being willing to give those weapons up.

Mr Pompeo said there would need to be "complete" and "verifiable" denuclearisation that would remove North Korea as a threat to the South, the United States and the rest of the world. He said a massive 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," Mr Pompeo said, though he declined to offer more detail.

AP