An inter-Korean summit would be the third of its kind, after Kim's father and predecessor Kim Jong Il met the South's Kim Dae-Jung and Roh Moo-hyun in 2000 and 2007 respectively, both of them in Pyongchang.
After months of silence on whether it would even take part in the Pyeongchang Winter Olympics in the South, which had their opening ceremony yesterday, nuclear-armed North Korea has gone on a charm offensive, dispatching athletes, performers and Kim's sister plus other diplomatic delegates to the South.
She verbally conveyed Kim's invitation to Moon "to visit the North at his most convenient time", he added.
Moon has long argued for engagement with the North to bring it to the negotiating table over its nuclear ambitions but did not immediately accept the offer.
"It is absolutely necessary for the North and the United States to engage in talks at an early date," he cited Moon as saying.