But later that evening, North Korean leader Kim Jong Un issued a statement saying that he would still be open to meeting with Trump and American officials.
Moon will brief the media on the unexpected meeting at 10 a.m. Sunday, his office said.
Moon and Kim met just north of the heavily militarised border in the afternoon to exchange views to pave way for a summit between North Korea and the United States, South Korea's presidential office said.
This rings especially true now that U.S. President Donald Trump has announced he's cancelled his Singapore summit with Kim, which was aimed at reaching an agreement on North Korea's nuclear ambitions.
"We are having very productive talks with North Korea about reinstating the Summit which, if it does happen, will likely remain in Singapore on the same date, June 12th., and, if necessary, will be extended beyond that date", Trump wrote in a tweet late Friday. On Thursday, White House officials had noted that Trump had left the door open with a letter to Kim that blamed "tremendous anger and open hostility" by Pyongyang but also urged Kim to call him.
Third, Trump must explain to Kim that there will be no letup in planned U.S.
That caution was absent in public remarks from U.S. officials on Friday, including Defense Secretary James Mattis, who told reporters the summit may be "back on". "I believe one of the keys to the peace and stability of the peninsula is the US-DPRK relations, and a summit between them is essential". At one point, Trump sought to remind Kim that the US nuclear arsenal was much more "massive and powerful" than that of North Korea. But Moon, the son of North Korean war refugees who rose to power previous year and has staked his presidency on the prospect of inter-Korean peace, might also be trying to secure his own commitments from the North - even if talks with Trump go nowhere.
Mr Trump said he was still carrying out talks with the North Korean leader, hinting the two might plan a meeting at a further date in a weird u-turn.
South Korea's presidential Blue House said the two leaders held talks for two hours on Saturday afternoon in the same Panmunjom truce village where they had met last month, making a declaration vowing to improve ties.
Early on Friday, Trump said the United States was again "talking to" North Korea. In the first year of Donald Trump's presidency, Pyongyang made this reality abundantly clear by carrying out its sixth (and most powerful) nuclear test and a number of ballistic-missile launches.
Yesterday, in a letter to Kim, Trump announced that he was cancelling their June 12 summit meeting in Singapore. In many respects, that could be the simplest of explanations as to why Kim Jong-un has offered, and President Trump has accepted, to meet to negotiate what could be the greatest diplomatic opening since Nixon went to China in 1972. "We would like to make known to the U.S. side once again that we have the intent to sit with the USA side to solve problem (s) regardless of ways at any time", he said to his official state media.
"We reiterate to the USA that there is a willingness to sit down at any time, in any way, to solve the problem", Vice Foreign Minister Kim Kye Gwan said in a statement carried by state-run media.
"It's a fortunate thing that the possibility of the North Korea-U.S. dialogue is still alive without being terminated", the South's Yonhap news agency quoted spokesman Kim Eui-kyeom as saying.
Moon has been careful during the last few months of whirlwind diplomacy to frequently credit Trump for the opening of talks with North Korea.
But despite the will on all sides for the summit to go forward, a fundamental gap exists between the United States' and North Korea's respective roadmaps to denuclearization. But North Korean state media, in a measured response, stated that they were still open to meeting the U.S. president.
In calling off the June 12 summit with Kim, Trump had accused the government in Pyongyang of "open hostility".