Kim's younger sister Kim Yo Jong -- one of his closest confidantes -- was part of the nuclear-armed North's diplomatic delegation to the Games that made worldwide headlines.
She delivered his invitation for the South's President Moon Jae-in to come to a summit in Pyongyang -- which he did not immediately accept, saying the "right conditions" were needed.
The North is subject to multiple sets of UN Security Council sanctions over its banned nuclear and ballistic missile programmes, and conducted dozens of weapons tests last year.
But the Winter Olympics in Pyeongchang have triggered extraordinary scenes, with Moon and Kim cheering a unified Korean women's ice hockey team together -- along with the North's ceremonial head of state Kim Yong Nam -- and attending a concert by Pyongyang's artistes.
Even so analysts warn that the positive mood could evaporate quickly after the Games, when the US and South are due to hold major joint military exercises that always infuriate the North.
Kim Jong Un met the delegation on Monday after it returned to Pyongyang, the official KCNA news agency reported.
It indirectly cited Kim as saying it was important to enhance "the warm climate of reconciliation and dialogue" created by the Winter Olympics -- which for months the North refused to say whether it would attend.
He gave instructions for "practical measures" to do so, it added, without giving details.
The South's appreciation of the North's presence and the welcome it gave its representatives were "impressive", he said, thanking Seoul for its "sincere efforts".
The KCNA report is the first official reaction from Kim -- the third generation of the dynasty to rule the isolated and impoverished North -- since his sister's charm offensive in the South.
Kim Yo Jong's visit made her the first member of the family to set foot in the country since the end of the Korean War.
Every detail of her trip was scrutinised, from the clothes she wore and her facial expressions to the bag she was carrying and even her handwriting.
But it left South Koreans divided, with some hoping it might usher in a real opportunity for reconciliation while others angrily burned the North Korean flag and criticised Moon for being too soft on Pyongyang.
How deep the rapprochement runs, how far it will go and how long it will last once the Games are over remain very open to question, analysts say.
Pyongyang's Olympic diplomacy has also highlighted differences between Seoul and its key protector the United States over how to handle the reclusive regime and its nuclear weapons programme.
Washington insists that Pyongyang must take concrete steps towards denuclearisation before any talks can begin, while Moon -- whose parents escaped from the North in a US evacuation during the war -- has long argued for closer involvement to bring it to the negotiating table.
Published : February 13, 2018
By : Agence France-Presse Seoul