The talks had been expected in the demilitarised zone on Thursday.
North Korea has imposed a testing moratorium, with the last missile test occurring on November 28, and it destroyed its main nuclear testing facility, although experts say those moves could be reversed.
Kim also agreed to repatriate remains of U.S. troops who died during the Korean War six decades ago. A total of 7,697 personnel remain unaccounted for from the Korean War.
"I deeply appreciate the energetic and extraordinary efforts made by Your Excellency Mr President for the improvement of relations between the two countries and the faithful implementation of the joint statement", he adds.
South Korean officials later said the meeting would be rescheduled for July 15, but that was after USA negotiators arrived Thursday at the militarized border between the two Koreas and were kept waiting, the Yonhap News Agency reported, citing diplomatic officials it didn't identify.
This would signal a shift in tone from Pyongyang's previous unwillingness to open up dialogue with Tokyo - which has been somewhat sidelined amid the flurry of diplomacy over North Korea's nuclear program, resulting in a recent thaw in relations between the North and the United States. Representatives of the two countries had been poised to meet in Panmunjom, which is regarded as the truce village on the inter-Korean border.
North Korean and U.S. teams, as well as United Nations officials, had been due to discuss the details of repatriation.More news: Armless transient man stabs tourist with scissors on South Beach
President Trump tweeted out the letter and an English translation on Thursday.
If realized, they will be the first general-level military talks between North Korea and the UNC since March 2009.
"Most important, instead of any hint of criticism of President Trump, the statement ends on a positive note: 'We still cherish our good faith in President Trump, ' underlining that the problem is not the President but rather 'headwind against the wills of the two top leaders...,'" he highlighted.
North Korea proposed to reschedule the meeting for Sunday.
North Korea's criticism of talks with Pompeo fueled further doubts about whether Trump will ever achieve his goal of "complete denuclearization", much less on the timeline of one to 2-1/2 years set out by various administration officials.
"Repatriation of US remains from North Korea will be important not just to American families, but to building trust between the USA and North Korea as well", Pompeo said earlier this week.
On Jun 20, Trump erroneously said 200 human remains had already "been sent back" from North Korea.