US Secretary of State Mike Pompeo says North Korean leader Kim Jong-un has agreed to allow inspectors into the country’s key nuclear and missile testing sites, following their meeting in the North’s capital, Pyongyang.

Pompeo, who had a short trip to the country on Sunday, told a news briefing in the South’s capital, Seoul, that international inspectors would be allowed access to 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,” Pompeo said before leaving for the Chinese capital, Beijing.

He said the two sides agreed to set up “working-level” negotiating teams to finalize the date and time for a summit between Kim and President Donald Trump, who met for the first time in Singapore in June.

Pompeo also met South Korean President Moon Jae-in in Seoul, and told him that his trip to Pyongyang was “another step forward” to denuclearization, but that there are still “many steps along the way.”

The visit to Pyongyang, the fourth this year, followed a stalemate in talks after the two sides agreed in Singapore to work toward denuclearization.

Thus far, the North has been taking several steps toward the goal, including the suspension of missile and nuclear tests, while the American side has taken no moves in return.

The North had denounced the US diplomat on his previous visit to Pyongyang in July, saying Pompeo was making “gangster-like demands.” The US diplomat did not meet Kim on that trip.

This time, however, Pyongyang’s reaction to the visit was positive. North Korea's official Korean Central News Agency (KCNA) cited Kim on Monday as saying, “Progress is being made implementing the decisions he reached with Trump in Singapore in June.”

“Kim Jong-un expressed satisfaction over the productive and wonderful talks with Mike Pompeo at which mutual stands were fully understood and opinions exchanged,” said the news agency.

It also confirmed that agreement had been reached to hold a second summit “as soon as possible.”

The state news agency did not mention any inspection-related issue, though.

Kim had agreed to allow the inspectors into country when he hosted Moon Jae-in last month in Pyongyang.

He also said he was prepared to permanently dismantle his country’s main nuclear site at Yongbyon, but only if the United States took “corresponding steps” to build trust.