"Also, thank you for your nice letter - l look forward to seeing you soon!"
The handover of the 55 caskets last Friday was part of the commitment Kim Jong-un made to Trump at the June 12th summit.
No date for a visit has been announced.
The return of the remains was one of Mr. Trump's conditions reached during the leaders' summit in June.
The U.S. military flew the remains from Osan Air Base in South Korea after they had undergone an initial review.
Each box was draped in a U.S. flag and carried off a military cargo jet by a sailor, a Marine, a soldier and an airman at Joint Base Pearl Harbor-Hickam in Honolulu on Wednesday. The return coincided with the 65th anniversary of the end of the Korean War. And that we'll bring our boys home, ' he said.
The White House did not provide details on the specific content of the letter from Kim, received Wednesday, or of Trump's reply. Other items on their joint memorandum, such as a pledge to "work toward complete denuclearization of the Korean peninsula", remain unaddressed.
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No policy changes came out of the summit, Mattis said on Friday, adding he had also not been given new direction on Syria. Putin said Friday that he was prepared to visit Trump in Washington and that he had also invited the president to Moscow.
USA spy satellites have detected fresh activity at the North Korean facility that produced its first intercontinental ballistic missiles.
Only one identification "dog tag" was delivered on by the North Koreans, complicating United States military efforts to identify the remains in the boxes.
"I think for the denuclearization to happen, we need to see the move and I haven't seen that yet".
Experts say positively identifying the decades-old remains could take anywhere from days to decades. He said during a Tuesday rally in Tampa, Florida, that the USA was "doing well" with North Korea and noted the return of detained Americans and Pyongyang's ceasing of nuclear testing and missile tests.
Trump in his tweet expressed gratitude to Kim "for keeping your word" on the return of the remains of more than 50 Americans service members killed during the Korean War. About 5,300 were lost in what is now North Korea.