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 speaks during a joint press conference with South Korean President Moon Jae-in at the Paekhwawon State Guesthouse in Pyongyang, North Korea, Sept. 19, 2018. "However, our hearts will become more open if we put in that much effort".
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.
The two neighbours technically remain at war after the 1950-53 Korean War ended with a ceasefire instead of a peace treaty.
The Cheong Wa Dae spokesman told reporters Kim "voiced his strong intention to visit Seoul while watching the situation".
Snow falling across Northland as winter storm moves in
The Minnesota Department of Transportation urged drivers to wait for conditions to improve if travel isn't necessary. To the south, heavy rains were forecast in the central Gulf Coast and stretching east to the mid-Atlantic.
"Kim also stated that he is willing to meet often with President Moon in 2019 to advance discussions of the peace and prosperity of the Korean Peninsula and to resolve together the issue of denuclearising the Korean Peninsula", said Kim Eui-kyeom.
Moon welcomed the latest message, saying the North's leader had also expressed "active intention to carry out agreements" made in his previous summits with the U.S. and the South, without elaborating further. 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.
Kim's New Year address provides a rare public appearance for the young leader and is closely watched by neighboring countries as it is seen setting the tone for his domestic and foreign policies.
Earlier this month, North Korea told the US that sanctions and pressure won't work to force Pyongyang into action on its nuclear program.
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.
The meetings followed a rollercoaster few years of relations between US President Donald Trump and Kim - nosediving with Trump's famous "Rocket man" speech at the United Nations General Assembly in 2017, and peaking with their highly anticipated summit in Singapore earlier this year.