"A very nice note from Chairman Kim of North Korea", Trump tweeted alongside a copy of the letter dated July 6 - the day that US Secretary of State Mike Pompeo landed in Pyongyang for what turned out to be hard talks with Kim's regime.
In it, Kim describes his landmark June 12 summit with Trump in Singapore as the "start of a meaningful journey" and expresses confidence that the "sincere efforts" of both sides "will surely come to fruition".
"I firmly believe that the strong will, honest efforts and unique approach of myself and Your Excellency Mr President aimed at opening up a new future between the DPRK and the USA will surely come to fruition", the North Korean leader wrote.
"I firmly believe that the strong will, honest efforts and unique approach of myself and Your Excellency Mr. President aimed at opening up a new future between the DPRK and the USA will surely come to fruition". Although Pompeo insisted progress continued to be made, North Korea accused the USA of making "gangster-like" demands.
Mr. Kim did not mention any commitments to the denuclearization process, generally commenting on wanting to improve relations between the two nations.
And even as Mr Trump released Kim's note, the United States was asking the UN Security Council to punish North Korea after finding that Pyongyang had violated restrictions on refined oil imports. "We will be ready", she told reporters aboard Pompeo's plane, as the top USA diplomat flew home to Washington after attending a North Atlantic Treaty Organisation summit.
In the joint statement, Kim committed to work towards the "complete denuclearization" of the Korean Peninsula in exchange for security guarantees from the U.S. Pompeo traveled to Pyongyang over the weekend to try to flesh out the deal, but apparently left with few tangible results.
North Korean officials denounced the meeting at its conclusion, accusing the US of having a "gangster-like" attitude in negotiations.
A statement by an unnamed foreign ministry official gave a starkly different account from one provided just hours before by US Secretary of State Mike Pompeo, who attended the talks.
Trump posted the letter, dated July 6, to Twitter on Thursday.
State Department spokeswoman Heather Nauert said North Korea called at midday Thursday and offered to meet on Sunday instead.
But North Korea's delegation failed show up.
The BBC reported speculation that North Korea may want payment for the return of the remains.
North Korea said Saturday it was seeking the "earliest start of the working-level talks" on the recovery of US remains. -North Korea relations worsened over North Korea's nuclear weapons program.