In his letter, which was written 24 days after the June 12 summit in Singapore, Kim addressed Mr Trump as "Your Excellency Mr President".
The Pentagon has shipped dozens of cases to Panmunjom in anticipation of receiving the remains of several US troops.
The source said that Kim did not see any need to hold dialogue with Japan before his summit with South Korean President Moon Jae-in in April, instead favoring relations with the United States, China and Russian Federation.
The two sides had been expected to discuss at the Korean Peninsula's demilitarized zone the return of US troop remains from the 1950-1953 war - an arrangement that the State Department had announced after Secretary Mike Pompeo's visit to Pyongyang last Friday and Saturday.
In fact, it appears to echo concerns that Trump did nothing more than give up a bunch of concessions without having Kim commit to a hardline stance on dismantling his country's nuclear ambitions.
The US military has since announced that 100 wooden coffins have been moved to the inter-Korean border in preparation. "We agreed to the denuclearization of North Korea".
What just happened in North Korea?
North Korea leader Kim Jong Un inspects Chunghung farm in Samjiyon County an undated photo released by North Korea's Korean Central News Agency on July 10.
North Korean negotiators failed to show up for scheduled talks with the U.S.at Panmunjeom, Thursday, on repatriating the remains of US soldiers killed in the 1950-53 Korean War, indicating a possible rift between the two countries in ongoing denuclearization talks.
There are about 7,700 United States soldiers classified as missing in action from the war. "Great progress being made".
Pompeo, speaking Wednesday to reporters as he arrived in Brussels for a NATO summit with President Donald Trump, said that change was up to North Koreans. The agreement reportedly covered the remains of some 200 American soldiers.
According to President Trump, returning the remains of USA troops was agreed upon during the Singapore summit. 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.
There was no call or explanation from North Korean officials on why they skipped the meeting.
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".