Trump's Twitter post on Thursday thanked Kim for returning the remains of some American war dead from the 1950-1953 Korean War. Vice-President Mike Pence and U.S. military leaders received the remains in Hawaii during a sombre ceremony on Wednesday.
The North Koreans provided enough specifics about where each suspected body was found that US officials have matched them to specific battles fought from 1950 to 1951, although not necessarily individuals, he said.
The latest letter from Kim arrived as concerns rise about North Korea's ballistic missile programme and commitment to denuclearisation. Much of that money was sent as reimbursement for the costs incurred during the recovery process, which for years involved North Korean officials accompanying American delegations as they traveled to war sites and obtained remains.
With the remains having been returned to the United States, the Defense P.O.W./M.I.A. Accounting Agency, a Department of Defense outfit, now has the hard task of identifying them, which could take months, according to The New York Times.
The Pentagon said last week it was considering the possibility of sending personnel to North Korea to search for additional remains.
The return of the remains was one of Mr. Trump's conditions reached during the leaders' summit in June.
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"I would go back in an instant if we were asked to", said Byrd who participated in numerous earlier search missions.
To work on the additional remains the team of DPAA researchers assigned to identifying the remains of Korean War missing will almost double in size from five to nine.
Most of the remains returned to the US were from the village of Sinheung Ri, near the Chosin Reservoir.
McKeague said he was "guardedly optimistic" that the repatriation would be the "first step of others to account for our missing from the Korean War".
"They had been very carefully packaged with padding and packaging that was done to I think a very high standard", Byrd said in a video call from Hawaii, where the DPAA has a large lab.
But other techniques such as comparing teeth to dental records and bones to chest X-rays are also used.
In addition, the 55 transfer cases handed over by the North Koreans contained equipment associated with the American military, such as boots, canteens, buttons and buckles, Byrd said.