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.

Wrapping up an extraordinary year in which the two leaders met three times, Kim shared his wish to go together towards peace and prosperity, according to Moon's office.

Kim added that he was sorry his plan to visit Seoul later this year -- in what was to be their fourth meeting of 2018 -- did not take place as agreed at their third summit in Pyongyang in September.

But he expressed a strong will to visit the South Korean capital in the future.

North Korean leader Kim Jong Un and South Korean President Moon Jae-in embrace at a summit in South Korea in April.

In response, Moon said on his social media account that he was "very glad" to see Kim's "willingness to meet often in the new year to resolve the practical issues of peace and prosperity and the denuclearization issue."

"If we meet together with sincerity, there is nothing we cannot achieve," added Moon. "It took a long time to get here and much has changed in one year."

The South Korean President said he hoped to see Kim in the new year, and that his welcome to the country "remains unchanged."