Moon and Kim met just north of the heavily militarised border in the afternoon to exchange views to pave way for a summit between the North and the United States, South Korea's presidential office said.
The Washington Post first reported that the team, which also included Allison Hooker, the Korea expert on the White House National Security Council, met with Choe Son Hui, the North Korean vice foreign minister.
South Korea's Moon will announce the outcome of his meeting with Kim on Sunday morning.
The Panmunjom Declaration was the result of the first meeting between Moon and Kim in April, and committed the two countries to denuclearization of the Peninsula and talks to bring a formal end to the Korean War.
The North Koreans were reacting to comments by Vice President Mike Pence suggesting that the rogue state could face a fate similar to that of Libya, where former leader Muammar Qaddafi was deposed and killed after agreeing to dispose of his nuclear weapons.
"There is ZERO disagreement within the Trump Administration as to how to deal with North Korea...and if there was, it wouldn't matter", Trump added via the social media platform.
Moon and Kim agreed at a surprise meeting on Saturday that a possible North Korea-US summit must be held successfully, Moon told a news conference in Seoul.
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Further, on Thursday, Trump wrote a letter to Kim in which he stated that due to North Korea's hostile behavior he may delay or cancel the summit. U.S. Defense Secretary Jim Mattis told reporters diplomats were "still at work" and said Trump had just sent a note out on the summit, which could be back on "if our diplomats can pull it off".
Trump, speaking Friday to graduates at the U.S. Naval Academy, did not mention North Korea directly, but he stressed the United States' military might.
"Our commitment to doing our best for the sake of peace and stability for the world and the Korean peninsula remains unchanged, and we are open-minded in giving time and opportunity to the USA".
Trump blamed the cancellation on the "tremendous anger and open hostility" in a recent statement by the North Koreans.
Trump and his team weathered insults, tolerated unanswered phone calls and waited hours for negotiating partners who never showed up as they sought to keep the planned Singapore summit with Kim on track.
In his letter, Trump warned Kim of the United States' greater nuclear might, reminiscent of the president's tweet past year asserting that he had a "much bigger" nuclear button than Kim.
The North Korean government on Friday said it is still "willing to give the US time and opportunities" to reconsider talks "at any time, at any format".
It was South Korean officials who first informed the USA earlier this year that Mr Kim was prepared to discuss potential nuclear disarmament. Libyan leader Muammar Gadafy was deposed and murdered by Nato-backed militants after halting his nascent nuclear programme.