The United States and its international partners are ready to provide North Korea with assurances if its leader Kim Jong-un is prepared to fully denuclearise the Korean Peninsula, a top American diplomat said on Saturday.

US Secretary of State Mike Pompeo, who returned from North Korea a day earlier after meeting with Kim, said he had a "good conversation" with the North Korean leader.

Talking to reporters at the Foggy Bottom headquarters of the US State Department, he said Donald Trump and the world have set the "conditions" for a successful outcome from the June 12 summit between the US President and Kim in Singapore.

Responding to a question about Kim's personality, Pompeo said, "You asked about my conversations with Chairman Kim. This question is sort of undignified. 'Is he rational'? Yes, we had good conversations, substantive conversations, conversations that involve deep, complex problems, challenges the strategic decision that Chairman Kim has before him about how it is he wishes to proceed and if he is prepared in exchange for the assurances that we're ready to provide to him if he is prepared to fully denuclearise.  And I'm not sure how to define it fully."

He said the US wants to ensure that its efforts yield the end result, that North Korea should not become a threat to the world.

"It's pretty clear what that means. It would be an activity that undertook to ensure that we didn't end up in the same place that we'd ended up before, or multiple passes at trying to solve this conundrum for the world, how to ensure that North Korea doesn't possess the capacity to threaten not only the US but the world with nuclear weapons," Pompeo said. 

"So, in order to achieve that, it will require a robust verification programme and one that we will undertake with partners around the world, which will achieve that outcome in a way that frankly no agreement before it has ever set forth. A big undertaking for sure, but one that Chairman Kim and I had the opportunity to have a good, sound discussion on so that I think we have a pretty good understanding between our two countries about what the shared objectives are," he said.

Pompeo said he had a "good" conversation with North Koreans and did his best to convey the US message to them.

"We were each representing our two countries, trying our best to make sure that we were communicating clearly, that we had a shared understanding about what our mutual objectives were. We had good conversations about the histories of our two nations, the challenges that we've had between us," he said.

"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," Pompeo added.

He was joined by his visiting South Korea counterpart Kang Kyung-wha.

The US and North Korea, Kang said, are "very clear" that the sanctions remain in place until and unless they see visible, meaningful action taken by North Korea to denuclearise. 

"The North Korean leader has committed to denuclearization, and formally so through the Panmunjom Declaration. We very much hope to see further steps, more concrete steps towards denuclearisation being produced at the US-North Korea summit.  So we're not talking about sanctions relief at this point," he said.