At the news conference in Pyongyang, Kim said he and Moon had "made a firm commitment to exert active efforts to make the Korean Peninsula free of nuclear weapons and nuclear threat and turn it into a land of peace".
Washington has demanded concrete action toward denuclearization, such as a full disclosure of North Korea's nuclear and missile facilities, before agreeing to key goals of Pyongyang, including an easing of worldwide sanctions and an official end to the Korean War.
But no details were agreed and Washington and Pyongyang have since sparred over what that means and how it will be achieved.
In the fraught process of North Korean denuclearization, Pyongyang has hit the ball firmly into the USA court by offering to welcome global inspectors to oversee the "permanent" dismantling of its missile-engine test site, and also to shut down its main nuclear complex at Yongbyon.
The South Korean president, Moon Jae-in, can be well satisfied with his third face-to-face meeting with Kim Jong-un in Pyongyang this week, which has brought relations between the two countries to their closest and warmest since the end of the Korean War.
North Korea has frozen missile and nuclear tests, blown up entrances to its underground nuclear test site and started the dismantling of a missile engine test facility.
According a joint statement signed by the countries' defense chiefs, the two Koreas agreed to establish buffer zones along their land and sea borders to reduce military tensions and prevent accidental clashes.
Later on Wednesday, Moon's delegation is scheduled to tour the Mansudae Art Studio, the North's largest producer of art and propaganda, which was sanctioned by the United Nations previous year.
Trump is struggling to convince Pyongyang to abandon its nuclear and missile programs without any preconditions, but the USA president tweeted the outcome of the latest summit was "Very exciting!" Kim's father, Kim Jong Il, agreed to visit Seoul, but never followed through.
Performers hold up cards to form patterns during the "Glorious Country" mass games held in conjunction with the 70th anniversary of North Korea's founding day in Pyongyang on September 9. Almost 3,000 journalists watched her giving directions to South Korean President Moon Jae-in himself as the two Korean leaders stood on stage facing North Korean honor guards.
If realized, Kim would be the first North Korean leader to visit Seoul since the peninsula was divided into North and South.
While the declaration appears to fall short of what Washington wants, President Donald Trump has maintained that he and Kim have a solid relationship and both leaders have expressed interest in meeting again after their June summit in Singapore.
"We are not afraid of future challenges", he said.
The neighbours have already agreed to withdraw some guard posts and equipment, in a bid to transform the world's most heavily fortified border into a no-weapons area.
United States officials involved in the latest negotiations have said North Korea has refused to even start discussions about defining denuclearisation.
Kim and South Korean President Moon Jae-in have been meeting in Pyongyang in an attempt to push forward their peace process, as well as advance dialogue with the United States. In a performance for the anniversary, a giant photo of Moon and Kim shaking hands at their first summit in April was projected onto one side of the stands in Pyongyang's 150,000-seat May Day Stadium.
Moon's spokesman, Yoon Young-chan, announced later in the day that the South Korean President would travel to the USA to meet with Trump on September 24. Within Trump's own administration, senior officials want North Korea to begin by declaring its nuclear and missile sites, rather than making piecemeal, unilateral concessions.