The general-level meeting between the United Nations Command and North Korea was the first of its kind since March 2009.
"Field guidance" visits by the leader are the mainstay of the North's state media output, with Kim regularly shown giving "on-the-spot guidance" to attentive officials, their notebooks in hand.
The report said the USA planned to send cases to the Demilitarized Zone and that North Korea would place the remains in them.
Major General Michael Minihan, chief of staff for the US-led UN Command, led the United States side and the North Korea's delegation reportedly included a two-star general.
In a statement, Secretary of State Mike Pompeo said the talks were "productive and cooperative and resulted in firm commitments".
The U.S. government estimates that the North Korean government has about 80,000 to 120,000 political prisoners in detention.
"We will be ready", she said.
"Working level meetings between US and North Korean officials will begin on Monday, July 16, to coordinate the next steps, including the transfer of remains already collected in the DPRK".
The talks took place at the inter-Korean border village of Panmunjom, reported Yonhap news agency.
Members of a pro-unification civic organization arrived in North Korea on Monday to discuss the return of remains of forced Korean laborers from the Japanese colonial era as well as other projects.
Experts are speculating that Pyongyang is trying to fast-track discussions on what it considers more critical issues, such as reaching a declaration to formally end the war, which stopped on an armistice and not a peace treaty.
The U.S. delegation was led by Maj.
The official told NK News, however, that the issue of whether or not the loading of cases on the North Korean side would be supervised had not yet been resolved. The White House has hailed the summit between Kim and Trump in Singapore as a major breakthrough toward disarming the isolated, nuclear-armed North in exchange for easing of sanctions and other help with economic development.
"Both sides agreed to re-commence field operations in the DPRK to search for the estimated 5,300 Americans who never returned home", Pompeo said.
The joint US-North Korea program to search for remains began in 1996 but was suspended in 2005 due to rising nuclear tensions.
He added that, based on the mood of talks so far, he expects the North Koreans to adhere to certain protocols which call for the respectful handling of the remains.