The repatriation of the remains of USA soldiers from North Korea has been a major issue between Washington and Pyongyang since the end of the Korean War, when thousands of Americans were left in Korea either missing in action or as prisoners of war.
Media reports following US Secretary of State Mike Pompeo's visit to Pyongyang last week painted a dire picture of denuclearization talks, seizing on a statement released by North Korea's Foreign Ministry decrying the Trump administration's "gangster-like" approach.
Pompeo characterized the talks as progressive, asserting that North Korea did not "push back" on denuclearization.
Ahead of the summit in Singapore, North Korean officials sometimes did not turn up to meetings where their US counterparts were expecting them, causing tension between the two negotiating partners.
North Korean officials didn't show up for a planned meeting with US counterparts to discuss returning the remains of American war dead, South Korean media reported, in the latest sign of tensions between the two sides.
The Singapore Declaration - the document President Trump signed jointly with Kim following their meeting in the country - reads in part, "the United States and the DPRK commit to recovering POW/MIA remains, including the immediate repatriation of those already identified".
An estimated 30,000 USA soldiers died in the 1950-53 Korean war.
"North Korea would have to deal with the consequences of breaking away from the negotiations if it were to do so, so it will likely not make an extreme decision", Kim said.
American officials have been on standby for weeks and have sent wooden coffins and flags to Panmunjom in preparation for a handover.
Meanwhile, the United Nations is trying to raise $US111 million ($150 million) to meet health, water and sanitation and food security needs for about 6 million people in North Korea.
Trump also announced that the US would suspend "war games" with South Korea.
There is speculation that North Korea may also want payment for the return of the remains, our correspondent says.
But he also acknowledged that a lot of work remained to be done, including on the issue of setting a timeline for denuclearization.
It would be the first such repatriation in more than a decade after a joint search effort was halted amid rising tensions over the North's nuclear weapons program.