Moon Jae-in and Kim Jong-un during a welcome parade when the pair met in Pyongyang, North Korea, earlier in 2018.
The report did not include details about the substance of the message but said they related to U.S-North Korea talks.
North Korean leader Kim Jong Un has sent a rare personal letter to his South Korean counterpart, President Moon Jae-in, expressing his willingness to meet again in 2019 and discuss denuclearization on the divided peninsula.
Kim had yet to confirm the timing of his unprecedented visit to Seoul, the South Korean capital, but the groups are already preparing for his arrival.
In his own message, Moon thanked Kim for his "warm" letter and said he was still invited to South Korea, according to the AP. But the US maintains it will keep sanctions in place against North Korea.
Kim was sorry his plan to visit Seoul this year did not take place as agreed at their third summit in Pyongyang in September, expressing his "strong resolve" to make it happen in the future while monitoring the situation, Moon's office said.
"Chairman Kim said he is willing to meet often with President Moon next year to move forward discussions on peace and prosperity and resolve the issue of denuclearization of the Korean peninsula", the spokesman said.
Moon Jae-in, in a message posted on Facebook, stressed Kim's willingness to comply with the South Korean and USA agreements on the issue, but acknowledged that many obstacles remain to be overcome.
The letter comes days before Kim is expected to address North Koreans in a New Year's speech that North Korean leaders traditionally use to announce major policy decisions and goals.
Post-summit nuclear talks between Washington and Pyongyang quickly settled into a stalemate as the countries struggled between the sequencing of the North's disarmament and the removal of US -led global sanctions against the North.
Kim used his New Year's speech a year ago to initiate diplomacy with Seoul and Washington, which led to his meetings with Moon and a historic June summit with Trump.
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