North Korea did not take kindly to the content of Pompeo's visit, which covered what the US definition of denuclearization is and what would be needed for sanctions relief.
North Korea's leader Kim Jong Un (4th R) and President Donald Trump (3rd L) attend a working lunch with their respective delegations at their historic US-North Korea summit, at the Capella Hotel on Sentosa island, June 12, 2018, in Singapore.
However, officials say it could be months before excavations can begin and years until the remains are identified.
Seoul's presidential office has said the suspension of the combined exercise could facilitate ongoing nuclear talks between North Korea and the United States.
North Korea said Saturday it was seeking the "earliest start of the working-level talks" on the recovery of USA remains.
State Department spokeswoman Heather Nauert told reporters in Tokyo on Saturday that the only thing Pompeo left behind in Pyongyang was a letter from Trump to Kim.
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While the summit represented a major thaw in relations, US sanctions on North Korea, among the most stringent in the world, will remain in place until the Kim regime implements "final, fully verified denuclearization", US State Secretary Mike Pompeo said last week.
Both sides were expected to discuss the timeline and ways in which remains of American soldiers would be returned at the meeting.
Pyongyang has reportedly asked the United Nations Command Armistice Commission to upgrade the talks to a higher level to include a US general, South Korea's foreign ministry said.
North Korea also proposed to reschedule the meeting for Sunday.
Trump faced a backlash for scrapping the drills, with critics saying he gave in too readily to Kim's request to halt the exercises while getting little in terms of tangible commitments from Pyongyang in return.
That number includes 7,702 who are missing in action, with an estimated 5,300 believed to have been lost in the North, according to the Hawaii-based DPAA, which oversees the effort.
Trump called Kim "Little Rocket Man" or "Rocket Man" in several tweets in 2017 and early 2018 and has said that North Korea's continued threats against the USA would be "met with fire and fury like the world has never seen".