Pompeo met with the North Korean leader in Pyongyang on Sunday to rekindle stalled denuclearisation talks following a landmark summit between Kim and US President Donald Trump in Singapore.

"Chairman Kim said he's ready to allow them to come in" to see the dismantled Punggye-ri nuclear test site, Pompeo said.

North Korea took apart the Punggye-ri facility in the country's northeast in May but has yet to allow international observers into the site to verify its claims.

The facility, buried inside a mountain near the border with China, was the staging ground for all six of the North's nuclear tests.

The inspectors will be allowed in as soon as the two sides agree on "logistics", Pompeo told reporters in Seoul before leaving for Beijing on a whirlwind diplomatic trip.

Denuclearisation of North Korea is "a long process", Pompeo said, adding: "We made significant progress."

The visit was Pompeo's fourth to North Korea.

Trump met Kim in Singapore in June for the first-ever summit between the two countries, resulting in what critics say was only a vague commitment by the North Korean leader towards denuclearisation.

The two sides have since sparred over the exact terms of the vaguely-worded deal, with the US pushing for a "final, fully verified denuclearisation" of North Korea while Pyongyang has slammed Washington for its "gangster-like" demands for its unilateral disarmament.