Kim first proposed a second meeting with Trump after their unprecedented June summit in Singapore.
Some senior South Korean officials accompanying Moon suggested inviting Kim and his wife to Mount Halla, the highest mountain and a scenic tourist resort in the South. That visit to the North Korean capital saw him again play the role of peacemaker as talks between the USA and North Korea appeared on the verge of collapsing.
They agreed that Kim would visit the South in the near future.
Both countries' defense chiefs also signed a 17-page accord in which the two countries vowed to "cease all hostile acts against each other".
North Koreans greet the convoy transporting South Korean President Moon Jae-in. Eastern Standard Time in the U.S. He tweeted again seven minutes later, "Also, North and South Korea will file a joint bid to host the 2032 Olympics".
"We should write another chapter of history between the North and the South by reflecting our new history on this Heaven Lake".
Remove 11 guard posts in the demilitarized zone by the end of the year.
While Pyongyang has stopped nuclear and missile tests this year, it failed to keep its pledge to allow global inspections of its dismantling of the Punggye-ri site in May, stirring criticism that the move could be reversed.
Analysts say the ball is now in Washington's court.
However, in the meantime Moon and Kim made concrete moves of their own to reduce tensions on their border.
But there have been concerns in South Korea and the United States that ending the war would ultimately prompt China and Russian Federation, if not North Korea, to demand that the United Nations Command (UNC), which overlaps with USA forces in South Korea, be disbanded and leave.
Shortly after the announcement, Trump called Wednesday's developments "very exciting" on Twitter.
"We have agreed to make the Korean Peninsula a land of peace that is free from nuclear weapons and nuclear threat", Kim said as he stood by Moon's side at the guesthouse where Moon is staying.
"They have continuously shown their trust towards one another and I hope there will be another summit between the two countries as soon as possible", Moon said.
Pompeo hopes to get back on track next week at the U.N. General Assembly meeting in NY, to which he's invited the North Korean foreign minister.
Kim and South Korean President Moon Jae-in flew separately to an airport near Mount Paektu on Thursday morning where they met up and drove to the mountain on the North Korean-Chinese border.
Moon, who set up the Singapore summit and is eager for another to happen, also told reporters that he'll convey to Trump his and Kim's desire to get a declaration on ending the Korean War by the end of this year.
For its part, Pyongyang - which wants a formal declaration the 1950-53 Korean War is over - has condemned demands for its unilateral disarmament as "gangster-like".
A big part of any negotiation to end the war would be the status of the thousands of U.S. troops stationed in South Korea as part of the two countries' alliance.
"A peace treaty would be sealed, as well as normalisation of North Korea-US relations, after the North achieves complete denuclearisation".