Moon's office said Kim also expressed regret that he couldn't make a planned visit to Seoul, South Korea's capital, by the end of December as pledged by the leaders during their last summit in September in Pyongyang, the North Korean capital. The Blue House didn't fully disclose Kim's letter.
"There will still be a lot of difficulties ahead," Moon said in his message. "However, our hearts will become more open if we put in that much effort. There's no change in our heart about welcoming Chairman Kim (to the South)."
The tweet also included a photo that showed a ruby-colored folder emblazoned with the seal of Pyongyang's powerful State Affairs Commission and the top part of Kim's letter, which started with: "Dear your excellency President Moon Jae-in. Our meeting in Pyongyang feels like yesterday but about 100 days have already passed and now we are at the close of an unforgettable 2018."
Through three summits between Moon and Kim this year, the Koreas agreed to a variety of goodwill gestures and vowed to resume economic cooperation when possible, voicing optimism that international sanctions could end to allow such activity.
The rivals have also taken steps to reduce their conventional military threat, such as removing mines and firearms from the border village of Panmunjom, destroying some front-line guard posts and creating buffer zones along their land and sea boundaries and a no-fly zone above the border.
"Chairman Kim said that the leaders by meeting three times in a single year and implementing bold measures to overcome the long period of conflict lifted our (Korean) nation from military tension and war fears," Kim Eui-kyeom, Moon's spokesman, said in a televised briefing.
"Chairman Kim said he will keep a close eye on the situation and expressed strong will to visit Seoul. ... Chairman Kim also expressed his intentions to meet President Moon frequently again in 2019 to advance discussions on the Korean Peninsula's peace and prosperity and discuss issues on the denuclearization of the Korean Peninsula," the spokesman said.
Moon's office did not reveal how Kim Jong Un's letter was delivered or whether he made any comments about his planned second summit with Trump in 2019.
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. In his meetings with Moon and Trump, Kim signed on to vague statements calling for a nuclear-free Korean Peninsula without describing when or how it would occur.
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 U.S.-led international sanctions against the North. There continue to be doubts about whether Kim will ever voluntarily relinquish his nukes, which he may see as his strongest guarantee of survival.
Kim and Trump are trying to arrange a second summit in early 2019.