Some remains have been returned to the USA over the years, but very few since recovery efforts were mostly halted in 2005 as U.S.
Doubts over the prospect of a breakthrough were further exacerbated following the secretary of state Mike Pompeo's overnight visit to Pyongyang last week, during which a promised meeting with Kim failed to materialize.
Mr Kim had agreed during the summit with President Trump to recover "POW/MIA remains, including the immediate repatriation of those already identified".
The US military has since announced that 100 wooden coffins have been moved to the inter-Korean border in preparation.
During Mr Pompeo's trip relations between the USA and North Korea appeared to take a dive as Pyongyang accused the United States of a "gangster-like mindset" during the high-level negotiations.
North Korean negotiators failed to show up for scheduled talks with the U.S.at Panmunjeom, Thursday, on repatriating the remains of US soldiers killed in the 1950-53 Korean War, indicating a possible rift between the two countries in ongoing denuclearization talks.
Mr Trump describes the letter as a "very nice note" and says, "Great progress being made!".
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Kim Jong Un put potatoes ahead of Mike Pompeo during a USA visit to agree denuclearisation details, state media has suggested.
There are about 7,700 U.S. soldiers classified as missing in action from the war.
Mr Pompeo had said progress was made during his two-day visit to Pyongyang.
"Most important, instead of any hint of criticism of President Trump, the statement ends on a positive note: 'We still cherish our good faith in President Trump, ' underlining that the problem is not the President but rather 'headwind against the wills of the two top leaders...,'" he highlighted.
With the meeting not taking place, the UNC reportedly made a phone call and North Koreans responded by saying that they needed to upgrade the "level" of the talks.
North Korea said Saturday it was seeking the "earliest start of the working-level talks" on the recovery of USA remains.
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 USA side.
"The U.S. side had had discussions with the North with an aim to hold the talks as early as July 12, but it appeared that the North was not ready for the talks", the source told Yonhap News Agency on condition of anonymity. Trump tweeted last September.