"Great progress being made", Trump tweeted on Thursday along with the letter, calling it a "very nice note from Chairman Kim".
The North Korean leader affirmed his firm belief that "the strong will, honest efforts and unique approach" the two have "aimed at opening up a new future between the DPRK and the USA will surely come to fruition".
This latest incident comes shortly after Pompeo's visit to Pyongyang resulted in North Korea accusing Pompeo of making a "unilateral and gangster-like demand for nuclearization".
Kim committed to "complete denuclearisation" when he and Trump met in Singapore last month.
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On a side table next to him were his favorite snacks: Doritos, a box of Chocolate Chip Crunch, and a bottle of soda. Renard was also pictured wearing his favourite player socks in a scene made to look like a typical, family home.
Trump has expressed an eagerness to tout the recovery of the war dead, telling Fox News that Kim was "giving us back the remains of probably 7,500 soldiers".
North Korean officials did not show up to a planned meeting with US officials at the demilitarized zone Thursday, where they were expected to continue discussions on repatriating the remains of Americans killed during the Korean War, a senior USA official tells CNN.
He was referring the summit statement signed by the two leaders - the first-ever US-North Korean summit - in which Kim agreed in broad terms to "work toward denuclearization" of the Korean Peninsula. "We will be ready". Trump tweeted on Thursday alongside a copy of the letter, dated July 6.
Attached were two images of the letter - one in Korean and the other an English translation.
A planned meeting Thursday between North Korean and US officials in the Demilitarized Zone between the two Koreas to discuss the return of the remains was postponed.
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That released Vettel into a lead he would hold to the end, while Hamilton forced his way inside Bottas at Brooklands a lap later. Bringing people closer to the sport is one thing, but asking them to help develop their sport is the next step.
One problem - no North Korean officials showed up, The New York Times reported. The U.S. also risks giving the North Koreans leverage to continue diplomacy and drag out disarmament talks. Reports say North Korea is now asking for higher-level talks for Sunday.
While the details are unclear, a setback on talks over the remains wouldn't bode well for broader negotiations about North Korea's nuclear program.
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State Department spokeswoman Heather Nauert said North Korea called at midday Thursday and offered to meet on Sunday instead.
Trump himself has remained upbeat about the outcome of the first summit between the leaders of the USA and North Korea.
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Clooney reportedly was in Sardinia filming a television miniseries adapted from Joseph Heller's Second World War novel Catch-22. Local media representatives who had gathered at the hospital said Clooney left in a van through a side exit.
A USA official waited at the border truce village of Panmunjom but no North Korean official showed up, South Korea's Yonhap news agency said, citing a Seoul diplomatic source.