It was the first time a member of the ruling Kim dynasty had visited the South since the 1950-1953 Korean War.
The report did not include details about the message but said it related to US-North Korea talks, and was conciliatory in tone.
South Korea's presidential spokesperson said a letter from the North Korean leader was delivered to South Korean President Moon Jae-in on Sunday afternoon.
In recent months, South Korean fan clubs of the leader have reportedly sprung up as the South anticipates frequent visits from as ties warm up between the two countries.
In a rare letter to Seoul, Mr Kim said he wished to pursue peace between the countries and "solve the issue of denuclearising the peninsula together", a spokesman for Mr Moon said.More news: Steve Alford out as UCLA basketball coach
The stalled negotiations have had an impact on inter-Korean ties, with Kim failing to visit Seoul this year as agreed to at an inter-Korean summit in Pyongyang in September.
In his letter, Kim said his landmark 2018 meetings with Moon - one in Pyongyang, and two at the truce village of Panmunjom, on the border between North and South - resulted in "practical and bold measures" to overcome long-standing confrontation and remove fears of war from the peninsula, according to Moon's spokesman.
"Even though there will be a lot of difficulties going forward, our hearts will be opened to each other depending on how much effort we make", he said in a statement posted on Facebook.
Kim also apparently sent an "amicable" letter to U.S. President Donald Trump.
Another speaker, in a reflection of the shift in perception towards Kim in South Korea, said: "Until now, we did not know Kim's true self".More news: North Korea warns of 'new path' if USA 'continues to break promises'
Talks between the US and North Korea have made little progress since Trump and Kim held an unprecedented summit in June and signed to "work toward complete denuclearization of the Korean Peninsula", without defining the term or setting a deadline.
"Chairman Kim said he will keep a close eye on the situation and expressed strong will to visit Seoul".
However, . Kim's letter to President Moon is expected to put inter-Korean diplomacy back on track, . with their next summit looking that much more likely to happen in Seoul.
The North Korean leader reached out to the South on Sunday night, . expressing his determination to make big strides toward denuclearization in 2019. There continue to be doubts about whether Kim will ever voluntarily relinquish his nukes, which he may see as his strongest guarantee of survival.More news: India cricket legend Sunil Gavaskar set to miss trophy presentation
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