Asia-Pacific

North Korea upbeat on Trump-Kim meeting

Donald Trump and Kim Jong Un have agreed to stay in touch. (AAP)

North Korean state media says Kim Jong Un and Donald Trump have agreed to keep in close touch and resume and push forward productive dialogues.

North Korean leader Kim Jong Un and US President Donald Trump have agreed to push forward dialogue for a new breakthrough in the denuclearisation of the Korean peninsula, North Korean state media says.

Trump became the first sitting US president to set foot in North Korea on Sunday when he met Kim in the Demilitarized Zone between the two Koreas and agreed to resume stalled nuclear talks.

"The top leaders of the two countries agreed to keep in close touch in the future, too, and resume and push forward productive dialogues for making a new breakthrough in the denuclearisation of the Korean peninsula and in the bilateral relations," KCNA news agency said on Tuesday.

The meeting, initiated by a Trump tweet Kim said took him by surprise, displayed the rapport between the two.

However analysts said they were no closer to narrowing the gap between their positions since they walked away from their summit in February in Vietnam.

US Secretary of State Mike Pompeo told reporters before departing South Korea new talks would likely happen "sometime in July ... probably in the next two or three weeks".

In a photo released by KCNA, North Korean Foreign Minister Ri Yong Ho and Pompeo are sitting next to Kim and Trump respectively in Freedom House, the building the two leaders had their one-on-one talks in.

KCNA said Trump and Kim explained "issues of easing tensions on the Korean peninsula," "issues of mutual concern and interest which become a stumbling block in solving those issues," and "voiced full understanding and sympathy."

Kim said it was the good personal relationship he had with Trump that made such a dramatic meeting possible at one day's notice and the relationship with Trump would continue to produce good results.

The two leaders' "bold, brave decision" that led to the historic meeting "created unprecedented trust between the two countries" that had been tangled in deeply rooted animosity, KCNA said.

UN Secretary-General Antonio Guterres says he "fully supports the continued efforts of the parties to establish new relations towards sustainable peace, security and complete and verifiable denuclearisation".

China also welcomed the meeting, describing it as "constructive and achieving positive results".

But problems could lie ahead.

"The fact the nuclear talks have jump-started is very encouraging but that doesn't mean the two sides have already adjusted their positions and set the conditions for successful working-level negotiations," said Korea National Diplomatic Academy professor Kim Hyun-wook.

After more than a year of talks, the two sides are still to agree a definition of denuclearisation, which North Korea has taken to include the US nuclear umbrella protecting Japan and South Korea, while Washington has demanded Pyongyang give up its nuclear weapons unilaterally.

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