"While delivering a letter from Kim Jong-un, chairman of the State Affairs Commission, which contained his stated willingness to improve South-North Korea relations, special envoy Kim Yo-jong orally delivered Chairman Kim Jong-un's invitation (for Moon) to visit the North at a time convenient to him, saying he is willing to meet President Moon Jae-in at the earliest date possible," the spokeswoman said in a statement.
Moon also stressed the need for North Korea to resume its dialogue with the United States.
The meeting in the Cheong Wa Dae was held in a "friendly" mood, where the two sides exchanged their views on a wide range of issues, including inter-Korean ties and other matters concerning the Korean Peninsula, according to the spokesperson.
There have been two inter-Korean summits so far, one in 2000 and an another in 2007. If Moon accepts the invitation, then this would pave the way for what could be the third meeting of the inter-Korean summits between the two countries.
Moon first met the delegation at the opening ceremony of the Pyeongchanger Winter Olympics, which was led by North Korean ceremonial leader Kim Yong-nam on Friday. He also had a three-hour meeting with the delegation as well.
Yong-nam is the President of the Presidium of the Supreme People's Assembly of North Korea.
Yo-jong's visit to the South was the first visit by a member of the ruling Kim family ever since the Korean War ended in 1953.
The meeting also included two other high-level delegates- Choe Hwi, the chairman of the National Sports Guidance Committee, and Ri Son-gwon, the head of the North Korea's state agency in charge of inter-Korean affairs.
The North Korean delegation's visit to South Korea was the first trip since August 2009, when a high-level North Korean delegation attended the funeral of former South Korean President Kim Dae-jung, who held the first-ever inter-Korean summit with then North Korean leader late Kim Jong-il in 2000.
After months of tensions, the athletes from the two countries marched under the same flag in the parade ceremony. A joint ice hockey team, comprising of both North and South Korean players will take part in the Winter Games.
Though South Korea is hosting the Winter Olympic Games for the first time, the nation has some experience in the world of international athletics, having hosted the 1988 Summer Games in Seoul.