The two leaders are midway through a three-day summit, which will see them address a number of other issues, the focus being nuclear disarmament.
But during their joint statement, South Korean president Moon took a second to state their intentions to make a joint bid to host the 2032 Olympics.
Moon also revealed that Kim has agreed to permanently dismantle a missile engine test site and launch pad in the presence of outside inspectors. If the US take corresponding measures, he will also destroy his main nuclear complex.
“We have agreed to make the Korean Peninsula a land of peace that is free from nuclear weapons and nuclear threat,” Kim added, as he stood by Moon’s side. “The road to our future will not always be smooth and we may face challenges and trials we can’t anticipate.
“But we aren’t afraid of headwinds because our strength will grow as we overcome each trial based on the strength of our nation.”
The day saw the pair finalise the joint statement together before delivering it in front of the press.
North Korea has been demanding a declaration formally ending the Korean War, which was stopped in 1953 by a ceasefire, but neither leader mentioned it as they read the joint statement.
Moon - who is now only the third South Korean leader to visit the North’s capital Pyongyang - invited Kim to visit Seoul, urging him to do so before the end of the year.
Moon’s two previous meetings with Kim have taken place at Panmunjom, a village on the border between the two countries.
President Trump has already praised the leaders’ move towards nuclear disarmament but made no mention of Kim’s call for the US to also take measures.
Kim gave the South Korean president an exceedingly warm welcome on Tuesday, the first day of the summit, meeting him and his wife at Pyongyang’s airport — itself a very unusual gesture — then riding into town with Moon in an open limousine.
The streets were lined with crowds of North Koreans, who cheered and waved the flag of their country and a blue-and-white flag that symbolises Korean unity.
The made-for-television welcome has become routine for their summits, after two meetings earlier this year.
The summit talks began at the ruling Workers’ Party headquarters where Kim and Moon were joined by two of their top deputies.
At the start of their meeting, Kim thanked Moon for brokering the June summit with Trump.
“It’s not too much to say that it’s Moon’s efforts that arranged a historic North Korea-US summit. Because of that, the regional political situation has been stabilised and more progress on North Korea-US ties is expected,” Kim said, according to South Korean media pool reports and Moon’s office.
Moon responded by expressing his own thanks to Kim for making a “bold decision” in a New Year’s speech to open a new era of detente and send a delegation to the South Korean Winter Olympics in February.