Vice President Mike Pence accepted the remains of presumed US soldiers killed during the war in a solemn ceremony at Joint Base Pearl Harbor-Hickam in Hawaii.
His comments came hours after Vice President Mike Pence presided over a ceremony in the state of Hawaii marking the repatriation of the 55 sets of remains to US soil.
"Chairman Kim made a commitment to denuclearize", Pompeo told reporters.
The White House did not provide details on the specific content of the letter from Kim, received Wednesday, or of Trump's reply. U.S. Marines also fought in the famous battle, but mainly along the reservoir's western side.
Other countries under the command of the United Nations also lost troops that are still unaccounted for, including the United Kingdom, Australia and Canada.
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"Some have called the Korean War the forgotten war", Pence said.
"Whosoever emerges from these aircraft, today begins a new season of hope for the families of our missing fallen", he said.
The U.S. military flew the remains from Osan Air Base in South Korea after they had undergone an initial field forensic review.
US Secretary of State Mike Pompeo was headed to an Asian security meeting in Singapore, where a meeting this weekend with North Korea's foreign minister was possible.
Byrd said the process to fully identify the remains, now more than 60 years old, could take anywhere from days to decades.
"We have remains that look to have been in a state of preservation consistent with coming from the Korean War era", he said, and materials provided with the remains included USA -issued military equipment such as canteens and buttons.
The U.S. ambassador also expressed skepticism regarding North Korea's dismantling of the Punggye-ri nuclear test site and the missile site at Tongchang-ri.
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The long-awaited repatriation comes after Trump first negotiated the deal at a landmark Singapore summit between the two leaders on June 12.
"I think it's going to work out very well", he told supporters at a rally in Tampa, Florida, on Tuesday night.
"I won't say anything about what they're doing on the ground because that would cause me to reveal intelligence sources", Hyten told reporters in a briefing.
Last Friday, . coinciding with the anniversary of the signing of Armistice Agreement, . Technically, the two Koreas are still at war.
The United States and North Korea conducted joint searches from 1996 until 2005, when Washington halted the operations, citing concerns about the safety of its personnel as Pyongyang stepped up its nuclear programme.
Iran, whose nuclear drive has also sparked worldwide alarm, and North Korea are reported to have a history of cooperation in military and missile technology.
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He said the Department of Defense was "taking active measures to protect election security including monitoring our adversaries". None of the intelligence officials, however, would be more specific on any Russian activity or on US efforts to combat it.