"I thought things would be odd and very different, but I found a lot of things being similar", Kim Yo-jong said while proposing a toast at last night's dinner, according to Moon's office.
Moon greeted and shook hands with Kim Yong Nam, president of the Presidium of the Supreme People's Assembly of the DPRK, at a reception for leader-level guests visiting the country to attend the opening ceremony of the 23rd Winter Olympics.
North Korea has said talks with its southern neighbour were "warm" but made no mention of inviting the South Korean president to a summit.
The United States insisted it would continue its policy of exerting global pressure on North Korea in an effort to get it to abandon its nuclear program.
He urged Pyongyang to abandon its nuclear ambitions permanently and reaffirmed the joint stance of the USA and South Korea towards the North.
"What we'd like to achieve, by coming to South Korea... is to show the world that this is what peace could look like when two leaders get along", Howard told the paper. He criticized the Trump administration for straining too hard to signal disgust of Kim Jong Un's government.
No Handshakes as Pence Avoids Kim Jong-un's Sister at Olympics
North and South Korea are technically still at war after their 1950-53 conflict ended in a truce rather than a peace treaty. Many observers remain suspicious of North Korea's intentions, given the regime's history of brutality and aggression.
The North has 22 athletes and hundreds of cheerleaders, performers and taekwondo demonstrators participating in Pyeongchang.
Moon has invited Kim and other senior North Korean officials to a luncheon at Seoul's presidential palace on Saturday.
U.S. Vice President Mike Pence met a group of North Korean defectors during the second day of his visit to South Korea, where he arrived on Thursday to attend the opening ceremony.
Pence did not directly address news of the invitation when asked.
Seoul's Unification Ministry said Friday that the Mangyongbong-92 will return to the North on Saturday.
The younger Kim, who came here as a special envoy of the DPRK leader, delivered the DPRK leader's invitation for Moon to visit Pyongyang at Moon's convenient time.
Pence did not interact with the North Koreans even though he was seated in the same box as them at Friday's opening ceremony.
North Korea has a track record of reaching out in talks following previous crises on the divided peninsula only to pull out after wresting concessions and aid from the West and analysts cautioned the rapprochement with the South may be short-lived.