SEOUL • South Korean President Moon Jae-in has voiced hopes that nuclear talks between North Korea and the United States will resume soon.
He also reiterated that Pyongyang is ready to accelerate the process of denuclearisation if Washington makes "corresponding measures".
But he declined to reveal what these steps could be, leaving Pyongyang and Washington to discuss them instead.
Experts said the "corresponding measures" are likely to refer to North Korea's persistent demand for a political declaration to end the 1950-1953 Korean War, which was halted by only an armistice.
Mr Moon said he will share undisclosed details from his conversations with Mr Kim with US President Donald Trump, when they meet at the United Nations General Assembly next week.
"If the US takes steps to end hostilities and start a new relationship with North Korea, the North is willing to expedite the denuclearisation process," he said at the summit press centre in Seoul.
Mr Moon returned to Seoul yesterday after a trip to Pyongyang for his third summit with Kim.
Nuclear talks had stalled for weeks over the lack of progress in denuclearisation. But Mr Kim's latest gestures appear to have mollified Washington.
Mr Trump praised the "tremendous progress" with North Korea, while US Secretary of State Mike Pompeo said they are ready to "engage immediately in talks to transform" relations with the regime.
Mr Pompeo also said he spoke to North Korean Foreign Minister Ri Yong Ho, and invited him to meet in New York on the sidelines of the UN General Assembly.
North Korean representatives have also been invited to meet the new US Special Representative for North Korea Stephen Biegun in Vienna "at the earliest opportunity", Mr Pompeo said in a statement.
Vienna is home to the International Atomic Energy Agency, whose inspectors may be involved in verifying the permanent dismantlement of the Dongchang-ri missile engine test site and launch pad, as Mr Kim pledged to do so in the Pyongyang Declaration signed with Mr Moon.
Experts said Mr Moon has proven once again that he can play a crucial role as mediator between the US and North Korea. The South Korean leader, who met Mr Kim in April and May this year, helped broker the historic Singapore summit in June between the US and North Korean leaders.
Mr Harry Kazianis, director of defence studies at the Washington-based Centre for the National Interest, noted how the mood in the Korean peninsula has changed in the past year. He said: "Missiles were going up in the sky last year, but now, Moon Jae-in is in Pyongyang addressing 150,000 people and looking like he's going to cry.
"He's really sincere in ending tensions in the Korean peninsula. You've got to give him credit for it."
Ajou University professor Kim Heung-kyu said there will be challenges ahead. "Moon's role puts him in a difficult position because of a trust deficit between the US and North Korea. He needs to balance the trust, otherwise it will be extremely difficult to proceed in negotiations."