Initial reports say the new remains appear to be in a similar state of disarray, meaning the identifying process could take years.
"One of the things that hasn't happened is the demonstrable moves toward denuclearization before we can entertain something like the end-of-war declaration", Harris said, according to Yonhap.
The return of the remains was agreed upon between President Trump and North Korean leader Kim Jong Un during their meeting in June.
Forensic experts will start work to identify the remains before returning them to their families.
Vice-President Mike Pence and the top commander of US forces in Asia, Adm. Phil Davidson, received the remains contained in 55 caskets during an emotional and solemn ceremony Wednesday after the caskets arrived by military cargo jets from South Korea.
The ambassador added a good starting point would be a North Korea list of nuclear facilities.
The White House is not addressing whether Trump and Kim may again meet.
Pence, in his address at Joint Base Pearl Harbor-Hickam in Hawaii, said he trusted that Americans killed in the war were among the flag-draped cases flown to Hawaii on Wednesday.
"Whosoever emerges from these aircraft today begins a new season of hope for the families of our missing fallen", Pence said.
The letter comes amid concerns over North Korea's ballistic missile program and commitment to denuclearization.
But the process could take anywhere from days, to decades.
North Korea may want to use the remains' return to keep diplomacy with the United States alive and win a reciprocal USA concession.
Air Force General John Hyten, who as commander of the U.S. Strategic Command oversees America's nuclear forces, said North Korea had clearly demonstrated its commitment to halt flight-testing missiles since none had launched since November. The two sides remain technically at war because a peace treaty was never signed.
The repatriation of United States remains was agreed by Mr Trump and Mr Kim after their June summit in Singapore.