North Korean leader 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.

South Korea’s President Moon Jae-in says he and Mr Kim spent most of the 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.

Mr Kim, who recently proposed another summit with Mr 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 United States 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, Mr Moon said.

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

Mr Moon said Mr 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.

US State Department spokeswoman Heather Nauert said Washington looked forward to a formal readout of the North-South talks in meetings with the South Koreans next week, which will include one between Mr Trump and Mr Moon on the sidelines of the UN General Assembly.

Mr Kim pledged to work toward the “complete denuclearisation of the Korean peninsula” during two meetings with Moon and his encounter with Mr Trump, but follow-up negotiations on how to implement the vague commitments have since faltered.

Washington calls for concrete action, such as a full disclosure of North Korea’s nuclear and missile facilities, before satisfying Pyongyang’s key demands, including an official end to the war and the easing of international sanctions.

The war ended in an armistice, rather than a peace treaty, meaning US-led United Nations forces, including South Korea, are technically still at war with the North.

But there have been concerns in South Korea and the US that ending the war would ultimately prompt China and Russia, if not North Korea, to demand that the United Nations Command (UNC), which overlaps with US forces in South Korea, be disbanded and leave.

-AAP