"After reading the letter, the Supreme Leader of the Party, the state and the armed forces said with satisfaction that the letter is of excellent content," the Korean Central News Agency said, referring to its leader.
"Appreciating the political judging faculty and extraordinary courage of President Trump, Kim Jong-un said that he would seriously contemplate the interesting content," it added.
The KCNA did not disclose when and how the letter was delivered to Kim, reports Yonhap News Agency.
The letter appears to be in response to the one Kim sent to Trump recently in time for the anniversary of their first-ever summit in Singapore last June.
Trump had described Kim's letter as "beautiful" and "very warm". He also emphasized that the relationship between them remains strong and that "something will happen that's going to be very positive".
The exchange of correspondence between the leaders renewed hopes for a resumption of denuclearization talks which have stalled since the breakdown of their second summit in February.
The summit collapsed as Pyongyang wanted sanctions relief as a corresponding measure in exchange for dismantling its Yongbyon nuclear complex, while Washington insisted that sanctions should remain in place until the North completely gives up its nuclear weapons programme.
( With inputs from IANS )