Just before departing Pyongyang, Pompeo said the meeting was set for July 12 but that it "could move by one day or two".
The White House had said earlier Pompeo would meet with the leader, but the encounter did not materialise and the top U.S. diplomat only met with Kim Yong Chol. "We will be ready". Representatives of the two countries had been poised to meet in Panmunjom, which is regarded as the truce village on the inter-Korean border.
Pompeo was in Pyongyang from Friday to Saturday to try to flesh out a bare bones denuclearisation deal made during last month's historic summit between Kim and US President Donald Trump.
An estimated 30,000 United States soldiers died in the 1950-53 Korean war. Remains brought to South Korea would then be transferred to Hawaii, where painstaking forensic work would be carried out to identify them.
There was widespread speculation that Pompeo would return with the remains following his visit to Pyongyang, but that did not happen. The U.S. filing blamed Russian Federation and China for selling oil products to Pyongyang.
North Korean officials did not turn up to a Thursday meeting with the US military about repatriating the remains of the war dead, according to a USA official with knowledge of the situation.
North Korean and USA teams, as well as United Nations officials, had been due to discuss the details of repatriation.
Pyongyang has already sent back the remains of 200 US troops, and the director of a USA defense agency said he is hopeful improved relations with North Korea will result in more recoveries.More news: Death toll mounts to 100 as Japan receives record rainfall
If realized, they will be the first general-level military talks between North Korea and the UNC since March 2009.
Earlier Thursday, Trump expressed optimism over the course of bilateral ties, despite concern in Washington and beyond that Kim may not abandon his nuclear weapons.
President Donald Trump shared what he described as a "very nice note" from North Korean dictator Kim Jong Un Thursday. Pompeo's trip made no visible progress towards either of those goals, but produced a conspicuous snub from Kim, who preferred his potatoes.
Speaking in Singapore on Thursday, South Korean President Moon Jae-in said that North Korea's statement was a "strategy that can often be seen in negotiations".
Dated July 6, the note was likely the one given to Pompeo during his visit to Pyongyang last week.
"The invariable trust and confidence in Your Excellency Mr President will be further strengthened in the future process of taking practical actions", he said.
Their meeting - the first between a sitting United States president and North Korea, led to claims that the latter would work towards dumping its nuclear weapons. But the agreement was terribly vague, and Trump ended up jettisoning a huge bargaining chip by voluntarily announcing an end to joint military exercises with South Korea, which always terrify North Korea.
Instead, North Korea appears as though it's conducting business as usual.