US Secretary of State Mike Pompeo has said that North Korean leader Kim Jong Un was ready to allow international inspectors into the North's nuclear and missile testing sites.

It is one of the main sticking points over an earlier denuclearisation pledge.

Mr Pompeo, who met Mr Kim during a short trip to Pyongyang yesterday, said the inspectors would visit a missile engine test facility and the Punggye-ri nuclear testing site as soon as the two sides agree on logistics.

"There's a lot of logistics that will be required to execute that," Mr Pompeo told a news briefing in Seoul before leaving for Beijing.

The top US diplomat also said both sides were "pretty close" to agreement on the details of a second summit, which Mr Kim proposed to US President Donald Trump in a letter last month.

Mr Trump and Mr Kim held an historic first summit in Singapore in June.

"Most importantly, both the leaders believe there's real progress that can be made, substantive progress that can be made at the next summit," Mr Pompeo said.

Stephen Biegun, new US nuclear envoy who was accompanying the secretary, said he offered yesterday to meet his counterpart, Vice Foreign Minister Choe Son Hui, "as soon as possible" and they were in discussion over specific dates and location.

Mr Pompeo's trip to Pyongyang, his fourth this year, followed a stalemate as North Korea resisted Washington's demands for irreversible steps to give up its nuclear arsenal, including a complete inventory of its weapons and facilities.

He told South Korean President Moon Jae-in yesterday his latest trip to Pyongyang was "another step forward" to denuclearisation but there are "many steps along the way".

At last month's inter-Korean summit, the North expressed its willingness to close the Yongbyon nuclear complex if Washington takes corresponding action, which Mr Moon said would include a declaration of an end to the 1950-53 Korean War.

Mr Pompeo declined to comment whether there was progress on a shutdown of the Yongbyon site.

Mr Moon also said North Korea will "permanently dismantle" its missile engine testing site and launch platform in the northwestern town of Tongchang-ri in the presence of experts from "concerned countries".

Donald Trump and Kim Jong Un met at a summit in Singapore last June

But Pyongyang failed to keep its pledge to allow international inspections of its demolition of the Punggye-ri site in May, fanning criticism that the move could be reversed.

In July, satellite imagery indicated the North has begun dismantling the engine test site in Tongchang-ri, but without allowing outsiders access for verification.

The Stimson Centre's 38 North said last week that no dismantling activity was spotted since 3 August.

Satellite image courtesy of Airbus Defense and Space and 38 North shows the Sohae Satellite Launching Station

Some experts say that opening the Tongchang-ri or Punggye-ri sites for inspection could be a goodwill gesture but has little significance in quickening denuclearisation.

State Department spokeswoman Heather Nauert said in a statement Mr Kim had invited inspectors to visit the Punggye-ri nuclear test site to confirm it had been irreversibly dismantled.

The statement did not provide further details.

In a more upbeat note, Pyongyang's state media said Mr Kim lauded his talks with Mr Pompeo, where Mr Kim "explained in detail the proposals for solving the denuclearisation issue".

"Kim Jong Un expressed satisfaction over the productive and wonderful talks with Mike Pompeo at which mutual stands were fully understood and opinions exchanged," North Korean news agency KCNA said.

Mr Kim said the bilateral dialogue would continue to develop "based on the deep confidence between the two leaders", and expressed gratitude to Mr Trump for making a sincere effort to implement the agreement made at their June summit, KCNA said.

KCNA also said the two sides agreed to hold working negotiations for the second summit as early as possible. But it did not mention any inspection-related issue.

Commenting on Mr Pompeo's meeting with Mr Kim, South Korean President Moon Jae-in said Mr Kim was expected to visit Russia soon.

He said Chinese leader Xi Jinping was also expected to travel to North Korea but did not elaborate further.

North Korea's state newspaper, Rodong Sinmun, featured eight photos of the meeting on its front page, including shots of Mr Kim and Mr Pompeo smiling and shaking hands, as well as some with Mr Kim's sister Kim Yo Jong.

North Korea denounced Mr Pompeo on his previous trip to Pyongyang in July for making "gangster-like demands". Mr Pompeo did not meet Mr Kim on that trip.