It continued, "The significant first meeting with Your Excellency and the joint statement that we signed together in Singapore 24 days ago was indeed the start of a meaningful journey".
At high-level talks last week, North Korea and the USA confirmed they are still poles apart on the next steps to be taken in the process.
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.
That was the day Secretary of State Mike Pompeo arrived for two days of meetings with top North Korean officials, which ended on a sour note after Pyongyang blasted the USA side for issuing a "unilateral and gangster-like demand for denuclearization".
While recovering the war dead would provide Trump a political victory similar to Kim's May release of three American detainees, it would do little to advance the goal of dismantling the regime's weapons program.
American officials have been on standby for weeks and have sent wooden coffins and flags to Panmunjom in preparation for a handover. But the president's optimistic outlook about North Korea's willingness to denuclearize and steps in that direction have been brought into question, after an NBC report claiming North Korea has been expanding a nuclear facility. The U.S. also risks giving the North Koreans leverage to continue diplomacy and drag out disarmament talks.
The meeting served as the highest-level platform for ongoing, unprecedented peace talks between the Cold War-era foes.
The most contrarian nugget of Carlin's analysis was his assertion that the statement, and North Korean domestic media's coverage of the visit, suggests progress was made.
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Trump was in London to meet with United Kingdom leaders after leaving the North Atlantic Treaty Organisation summit in Brussels, Belgium, when he tweeted Kim's letter.
But skepticism remains over whether North Korea's findings will satisfy Japan.
There are about 7,700 United States soldiers classified as missing in action from the war.
The President released the letter in Korean with an English translation.
Despite that, Trump hailed the July 6 letter as a "very nice note", saying "Great progress being made".
"The U.S. side had had discussions with the North with an aim to hold the talks as early as July 12, but it appeared that the North was not ready for the talks", the source told Yonhap News Agency on condition of anonymity.
Although KCNA did not say when the trip was made, Kim Yong Chol told a visiting Seoul official last week that the leader was away for a trip to a "local region".