The invitation to visit Pyongyang at the "earliest date" was delivered by Kim's sister Kim Yo Jong, the Yonhap news agency reported citing presidential administration.
Kim Yo Jong is a member of the North Korean government delegation that arrived at the opening of the Olympics in Pyeongchang. On Saturday morning she, along with other high-ranking members of the delegation, visited the presidential palace and attended a dinner hosted by the President of South Korea. According to the agency, the delegates were invited in person.
"Let us make it happen by creating the necessary conditions in the future," Moon was quoted as saying by presidential administration's spokeswoman, according to the Yonhap news agency.
"An early resumption of dialogue between the United States and the North is needed also for the development of the South-North Korean relationship," Moon's quote read further.
A visit by Moon to the North would enable the first summit between leaders from the two Koreas since 2007.