Mr. Trump said he received "a very nice note" from Mr. Kim on Twitter.
The release of the letter comes amid growing skepticism around Pyongyang's willingness to denuclearize.
When relations between Kim and South Korea, and then the United States, seemed to thaw, those three banks notified South Korean Deputy Prime Minister Kim Dong-yeon last month of their willingness to participate in North Korea's economic development, according to a report in the Korea Times.
While the American officials clearly thought a meeting was scheduled, Secretary of State Mike Pompeo had previously indicated that the details hadn't been settled before he left North Korea on Saturday.
North Korea has reportedly proposed holding general-level military talks with the UNC over the repatriation of remains, sources here said Thursday, after it failed to show up at the meeting earlier that day. About 100 wooden transport cases were sent to the DMZ in recent weeks to prepare for receiving U.S. troop remains.
Following the North Koreans' no-show at Thursday's meeting, the U.S. state department said the two delegations had agreed to meet on 15 July.
Pompeo insisted the talks were making progress but as soon as he left, the North's foreign ministry berated him over his "unilateral and gangster-like" demands and for offering no constructive steps on the United States side.More news: Puerto Rican T-shirt video controversy results in officer's resignation
When the two leaders warmly shook hands in Singapore a month ago, it appeared that a resolution to the North Korean nuclear standoff and normalization of bilateral ties would progress quickly.
The Trump administration has insisted that progress is being made.
Trump tweeted accompanying a Korean and English version of the note from Kim. A total of 7,697 personnel remain unaccounted for from the Korean War. Pyongyang has asked the UN Command Armistice Commission to upgrade the talks to a higher level to include a US general, South Korea's foreign ministry said.
North Korean representatives didn't show up for scheduled talks with the US about returning the remains of fallen American soldiers.
"Just heard Foreign Minister of North Korea speak at U.N. If he echoes thoughts of Little Rocket Man, they won't be around much longer!"
"The US is fatally mistaken if it went to the extent of regarding that the [Democratic People's Republic of Korea] would be compelled to accept, out of its patience, the demands reflecting its gangster-like mindset", Pyongyang cautioned.
For decades, the United States would not talk to North Korea, which has killed foreign and U.S. citizens while maintaining one of the worst human rights regimes on earth, without a concrete path towards dismantling the country's nuclear weapons.