Moon made the comments to the daughter of U.S. President Donald Trump, Ivanka, who arrived in South Korea on Friday to attend the Pyeongchang Olympics closing ceremony.
Ivanka Trump is scheduled to have dinner with South Korean President Moon Jae-in later in the day.
A high-level North Korean delegation will also attend Sunday's Olympic closing ceremony, but the South Korean government said it's unlikely that Ivanka Trump will meet the North Koreans.
Moon expressed his gratitude towards President Donald Trump, saying ongoing talks with North Korea were thanks to Trump's "strong support". "We are very, very excited to attend the 2018 Winter Olympic Games, to cheer for team United States of America and to reaffirm our strong and enduring commitment to the people of the Republic of Korea".
It emerged this week Pence was supposed to meet North Korean officials during his time in South Korea, but the meeting was called off by Pyongyang at the last minute.
South Korea's Unification Ministry said.
"If our government helps her understand South Korea's situation on the peninsula, it could help improve Seoul-Washington ties", the paper wrote. Earlier this week, the US government said Vice President Mike Pence was set to meet North Korean officials during his visit to South Korea for the opening ceremony, but that North Korea canceled at the last minute.
There are no indications that Ivanka Trump will meet Kim Yong Chol, vice chairman of North Korea's ruling Workers' Party Central Committee, who is to lead the North's delegation to the closing ceremony. -North Korean dialogue as needed before he agrees to seeing Kim Jong-Un in Pyongyang.
Kim is the former chief of North Korea's Reconnaissance Bureau, widely considered to be responsible for a torpedo attack against a South Korean warship in 2010 that killed 46 sailors.
As CBS News' Jacqueline Alemany reported earlier this week, Ivanka Trump's visit to the Olympics was described by White House officials in dramatically different terms than Pence's politically charged trip.
While Pence attended the Winter Games accompanied, as usual, by his wife, Karen Pence, there was no sign of Jared Kushner as Trump landed at Incheon airport with White House press secretary Sarah Sanders in tow.
The White House has emphasized that the objective of her visit is to celebrate the achievements of the athletes, noting that she is a winter sports enthusiast herself. He may even extend his own invitation for Moon to see him in Washington while Moon considers his response to Kim Jong-Un's letter, delivered by his sister when she saw him at the Blue House the day after attending the opening ceremonies.
"At the closing ceremony their lines of movement will not cross", a senior official of Seoul's presidential Blue House told Yonhap news agency. An official described Ivanka Trump as well suited to lead the delegation because of her experience on the world stage, and because she is "something of a winter sports enthusiast".