North Korea will allow experts from "concerned countries" to watch the closure of its missile engine testing site and launch pad at Tongchang-ri, Moon said at a joint news conference with Kim after their meeting in the North Korean capital.
North Korea's two previous leaders, Kim's grandfather and father, are said to have been born in its shadow.
But while Moon's warm reception in the North Korean capital and smiling photo opportunities have already been considered a diplomatic victory, a number of worldwide policy experts are still uncertain as to whether facility shutdowns in Yongbyon will actually cease all nuclear production, with the Times noting that some foreign analysts suspect that Kim has other nuclear programs operating in secret. Compared to the vague language of their two earlier summits, Kim and Moon seem to have agreed on an ambitious program meant to tackle soaring tensions previous year that had many fearing war as the North tested a string of increasingly powerful weapons.
A former human rights lawyer, he said in a 2017 book published months before his election as president that he wanted to "finish his life" in his mother's North Korean hometown doing pro-bono service.
"Pyongyang joint declaration did not include any of those specific measures of North Korea and the corresponding actions of the US".
Mr Moon told reporters in Seoul that he will carry a private message from Mr Kim for Mr Trump on the nuclear standoff when he meets with the U.S. president in NY next week on the sidelines of the UN General Assembly session.
On Wednesday, Kim also said he plans to visit Seoul "in the near future" - a trip that would be historic in the relationship of these two countries that technically remain at war.
Talks between the USA and North Korea have stalled in recent weeks after President Trump became uncertain that Kim was following through with pledges made at their Singapore summit in June.
But commentators in the US immediately expressed skepticism, though they pointed out that Trump's very hyperbole could also pave the way for a second summit that might then produce more palpable results.
Washington has demanded concrete action, such as a full disclosure of North Korea's nuclear and missile facilities, before agreeing to Pyongyang's key goals, including an easing of worldwide sanctions and an official end to the Korean War. North Koreans are not going to act unilaterally, unconditionally.
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.
Secretary of State Mike Pompeo says he has invited North Korea's foreign minister to meet with him next week to continue discussions on efforts to get the North to abandon its nuclear weapons.
With the main business of the day over, North Korea was expected to hold a huge mass games spectacle in the evening, with Moon as the special guest.
On Thursday, Moon and Kim, accompanied by their wives, visited Mount Paektu on the Chinese border. North Korea wants South Korea and the United States to declare the war to be formally over, as a sign that hostilities have ended and to build trust.
The question is whether it would be enough for US President Donald Trump to pick up where Moon has left off.
In the meantime, however, Moon and Kim made concrete moves of their own to reduce tensions on their border.
"Invoking the end of Trump's term in January 2021 is another way of saying to the North that American patience is not unlimited and that Kim Jong Un won't be able to sidestep denuclearisation indefinitely", Russel added.