The outcome of their surprise meeting, which was held in the truce village of Panmunjom and lasted for two hours, is going to be revealed by Mr Moon on Sunday.
South Korean officials have said the pair discussed carrying out the peace commitments agreed in their first summit last month, as well as Mr Kim’s potential meeting with US President Donald Trump.
It follows a whirlwind 24 hours which saw Mr Trump cancel his highly anticipated meeting with the North Korean leader, which was due to take place on 12 June.
However, the US president later tweeted that the summit could be back on and held in Singapore as originally planned – with Seoul expressing relief that the prospect of talks had been revived.
The Blue House, South Korea’s presidential office, said in a statement: “They exchanged views and discussed ways to implement the Panmunjom Declaration and to ensure a successful US-North Korea summit.”
Pictures from the summit show Mr Moon and Mr Kim shaking hands as well as embracing, and reveal Mr Kim brought along his sister, Kim Yo Jung.
She has played a major public role in talks with the south and led the delegation to the Winter Olympics in February.
Mr Trump’s decision to pull the summit is understood to have followed comments from North Korean diplomat Choe Son Hui, who referred to Mike Pence as a “political dummy”.
She also said it was up to the Americans whether they would “meet us at a meeting room or encounter us at nuclear-to-nuclear showdown”.
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Despite the cancellation of the summit, the North Korean government responded with some restraint, saying: “The first meeting would not solve all, but solving even one at a time in a phased way would make the relations get better rather than making them get worse.”
The Vice Foreign Minister Kim Kye Gwan said the meeting could happen “any time, in any format”.