North Korea’s Kim Jong Un wants a second summit with US President Donald Trump soon to hasten denuclearisation, but a key goal is declaring an end this year to the 1950-53 Korean War, the South’s President Moon Jae-in said on Thursday.

Moon said he and Kim spent most of a three-day summit discussing how to break an impasse and restart nuclear talks between Pyongyang and Washington, which are at odds over which should come first, denuclearisation or ending the war.

Kim, who recently proposed another summit with Trump after their unprecedented June talks in Singapore, said the North was willing to “permanently dismantle” key missile facilities in the presence of outside experts, and the Yongbyon main nuclear complex, if the US took corresponding action.

The joint statement from the summit stipulates his commitment to a “verifiable, irreversible dismantlement” of the nuclear programmes, and ending the war would be a first US reciprocal step, Moon said.

“Chairman Kim expressed his wish that he wanted to complete denuclearisation quickly and focus on economic development,” Moon told a news conference in Seoul, shortly after returning from the summit with Kim in Pyongyang.

“He hoped a second summit with Trump would take place in the near future, in order to move the denuclearisation process along quickly.”

Moon said Kim was also open to inspection of a nuclear test site in the northwest town of Punggye-ri, which he called the North’s sole existing facility for underground detonations.

While Pyongyang has stopped nuclear and missile tests this year, it failed to keep its pledge to allow international inspections of its dismantling of the Punggye-ri site in May, stirring criticism that the move could be reversed.

Representatives of the White House and the US State Department did not immediately respond to a request for comment.

But US Secretary of State Mike Pompeo said on Wednesday he had invited the North’s foreign minister to meet in New York next week and other Pyongyang officials to Vienna for talks with nuclear envoy Stephen Biegun.