The delegation of 22 officials from the North arrived on Friday in order to attend the opening ceremony for the Winter Olympics.
Any meeting would represent a diplomatic coup for Moon, who swept to power previous year on a policy of engaging more with the reclusive North.
They capped their final day in South Korea by joining Moon at a Seoul concert given by a visiting North Korean art troupe led by the head of the immensely popular Moranbong band, whose young female members are hand-picked by Kim Jong Un.
But US Vice President Mike Pence, who was seated in the same box at the opening ceremony, did not interact with the North Koreans at any point, US officials said.
Washington and Seoul have agreed to suspend their joint military drills until the end of South Korea's Pyeongchang Winter Paralympics on March 18, to which North Korea has pledged to send its athletes.
Some North Korean experts believe tough United Nations sanctions that are cutting off most of the isolated North's sources of revenue have added pressure on Pyongyang to engage further with Seoul.
"Honestly, I didn't know I would come here so suddenly".
"We hope that President (Moon) could leave a legacy that would last over generations by leading the way in opening a new era of unification", she said, according to Moon's office.
President Donald Trump and South Korea's President Moon Jae-in shake hands during a meeting at South Korea's presidential Blue House in Seoul, South Korea, November 7, 2017.
On Wednesday, Pence announced the "toughest" round of sanctions yet targeting North Korea at a news conference alongside Japan's Prime Minister Shinzo Abe.
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North and South Korea are technically still at war after their 1950-53 conflict ended in a truce rather than a peace treaty.
South Korea's Unification Ministry spokesman Baik Tae-hyun told a regular briefing Seoul was still in close consultations with the United States over its North Korea policy.
North Korea has made clear that it does not intend to negotiate away its nuclear and missile programs in return for relief from worldwide sanctions. Analysts say that the missiles, which were successfully flight tested three times a year ago, could potentially reach deep into the USA mainland when perfected. But the prospect could sow division between the dovish leader, who has long argued for engagement with the nuclear-armed North to bring it to the negotiating table, and US President Donald Trump, who past year traded personal insults and threats of war with Kim.
"Moon is saying that although he is keen to reboot inter-Korean relations, the dialogue between the United States and the North is essential".
"(The visit) shows North Korea's will to improve inter-Korean ties is very strong and if needed it will take unprecedented and aggressive measures", the ministry said.
South Korean President Moon Jae-in had "virtually accepted" North Korean leader Kim Jong Un's invitation to Pyongyang, officials said on Saturday, making way for a first inter-Korean summit in more than a decade.
The two Koreas have a rocky and sometimes violent history at the Blue House.
Kim Jong Il traveled to Beijing to meet then Chinese president Jiang Zemin before the summit.
The delegations shared a lunch of dried pollack dumpling soup, a regional specialty of the only divided province on the Korean peninsula, and soju, a spirit popular on both sides of the heavily militarized border.
The source said the trip would be "sometime after the Olympic Games", which are due to finish on February 25.