An agreement to return the remains of USA service members was touted by the Trump administration as one of the commitments secured during the president's historic summit with Kim on 12 June.
The Pentagon has shipped dozens of cases to Panmunjom in anticipation of receiving the remains of several US troops. The U.S. Embassy in Seoul said it had no immediate information.
The US military also announced that 100 wooden coffins had been dispatch to Panmunjom to receive the remains, although repatriation has yet to take place.
The U.S. says North Korea has continued to smuggle refined petroleum products into the country in excess of the quota of 500,000 barrels per year allowed under United Nations sanctions imposed because of nuclear and missile programs.
North Korean representatives didn't show up for scheduled talks with the US about returning the remains of fallen American soldiers. The discussions about returning Americans soldiers killed nearly 70 years ago was perhaps the most tangible outcome from Pompeo's trip, which analysts expected would at least secure the release of some remains.
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On Monday, the president shared his confidence that the North Korean leader would live up to the agreement both leaders signed in Singapore.
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".
The Trump administration has insisted that progress is being made.
"We have to see the USA defense ministry's response, but the UNC reportedly gave a positive signal to North Korea, so there is a good chance of the talks taking place on Sunday", the source said. On the day he left the North issued a statement on state-run media accusing the United States of "gangster-like" demands for unilateral disarmament.
Trump described the letter as a "very nice note" and said, "Great progress being made!". The expected North Korean officials never arrived, according to the official who requested anonymity as he was not permitted to talk publicly about the event.
Speaking to Fox News about the possibility of a Kim visit to the White House, Trump said last month that such a visit "could happen", and added that he and Kim "had good chemistry".