The group was among at least a dozen civic group, known collectively as the "Paektu Praise Committee" which have become an unofficial welcome group for Kim if he visits Seoul.
"There is a discourse channel between North Korea and the United States through which they trade dynamic correspondence, yet I can't know whether it appeared as letter or something different", Moon's representative told a news preparation on Monday.
The North Korean leader reached out to the South on Sunday night, . expressing his determination to make big strides toward denuclearization in 2019.
"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 Jong-un also "expressed an intention to meet with Moon frequently in 2019" to pursue peace and "solve the issue of denuclearising the peninsula together", the spokesman said. There's no change in our heart about welcoming Chairman Kim (to the South)'.
Trump said last week that he was "looking forward" to his second summit with Kim, which the USA says may take place early next year.
The tweet also included a photo that showed a ruby-coloured 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".
WHILE Kim Jong Un has always been regarded as a dictator in South Korea, the North Korean leader can expect a warm welcome from a portion of his estranged neighbours who have set up fan clubs in anticipation of his future visits.
Hours after its disclosure on Sunday, Moon hailed Kim's renewed commitment to denuclearization.
Denuclearization talks, however, have been in a stalemate as Pyongyang wants sanctions relief for subsequent steps following the summit, while Washington is asking for more concrete measures before making major concessions. 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 also agreed to improve relations when they met in June in Singapore.