"The significant first meeting with Your Excellency and the joint statement that we signed together in Singapore 24 days ago was indeed the start of a meaningful journey", reads the letter dated July 6.
The talks Sunday are expected to involve officials from the Pentagon and the U.N. Command, which commanded US -led allied forces during the war and is involved in maintaining the armistice that ended the fighting in 1953. The U.S. Embassy in Seoul said it had no immediate information.
The two sides had been expected to discuss at the Korean Peninsula's demilitarized zone the return of USA troop remains from the 1950-1953 war - an arrangement that the State Department had announced after Secretary Mike Pompeo's visit to Pyongyang last Friday and Saturday.
While recovering the war dead would provide Trump a political victory similar to Kim's May release of three American detainees, it would do little to advance the goal of dismantling the regime's weapons program.
Pompeo has insisted that a raft of tough economic sanctions imposed on North Korea would remain in place until "final, fully verified denuclearization" occurs.
North Korea has reportedly proposed holding general-level military talks with the United Nations Command (UNC) over the repatriation of remains of American troops killed during the 1950-53 Korean War, sources here said Thursday.
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While mean-spirited in name, the contest promotes advocacy and adoption for all dogs, regardless of how mangy the mutts may be. No pooch could beat out 9-year-old English bulldog " Zsa Zsa ", with an exceptionally droopy tongue.
He left with only an agreement to set up working groups to discuss aspects of the deal, including the planned meeting on returning the remains.
There are about 7,700 United States soldiers classified as missing in action from the war.
The North Korean leader also expressed optimism about a future meeting.
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.
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.
Trump agreed to halt bi-annual U.S. military exercises conducted with South Korean forces, while Kim made a vague commitment to denuclearization.
North Korea has imposed a testing moratorium, with the last missile test occurring on November 28, and it destroyed its main nuclear testing facility, although experts say those moves could be reversed.