Returning the remains was a commitment from the 12 June summit between Kim Jong-un and Donald Trump in Singapore.
"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", Mr Kim wrote, referring to North Korea by its acronym.
Pompeo was not granted an audience with Kim, and North Korea criticized US demands following the visit.
Earlier Thursday, a diplomatic source here said the US and North Korea were still in talks to set a date for working-level dialogue over the repatriation of remains of American troops.
Representatives of the USA and North Korea were expected to have working-level talks at the inter-Korean border truce village of Panmunjom on Thursday to hash out the details of the repatriation, but the discussions did not occur. Moreover, rumors are that the site in question is for liquid-fuel engines when the North has moved on to more sophisticated solid-fuel engine technology (liquid-fuel engines have longer launch times and therefore make them more susceptible to pre-emptive strike). But the North Korean leader never showed up during Pompeo's three-day visit. "We had anticipated the USA side would come with a constructive idea, thinking we would take something in return", a foreign ministry official said in a statement.
The meeting was to discuss repatriation of the remains of United States troops who died in the Korean War almost 70 years ago, another term agreed upon during the June 12 summit.
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.
In December the 15-member Security Council capped refined petroleum product exports to North Korea at 500,000 barrels a year. He has also been very clear since the 1990s that he does not understand why the United States bears costs for stationing troops in Korea when the Koreans are a "rich country" that can defend themselves.
The letter's date indicates it was written before Secretary of State Michael Pompeo's visit late last week to Pyongyang, where the U.S. and North Korea struggled to agree over plans to denuclearise the Korean peninsula. South Korea's Yonhap news agency, citing unnamed sources, said the North requested talks at a higher level.
"Both the U.S. and the North are still in discussion over when to meet", the official added.
But there's growing skepticism in Washington over the Trump administration's engagement with North Korea.
According to President Trump, returning the remains of US troops was agreed upon during the Singapore summit.
About 100 wooden transport cases were sent to the DMZ in recent weeks to prepare for receiving USA troop remains.