But while Pompeo on Saturday painted a positive picture of the follow-up talks, North Korean officials accused the United States of trying to unilaterally pressure their country into abandoning its nuclear programme.
Mr Kim made a broad commitment in Singapore to "work toward denuclearisation" but did not give details on how or when he would dismantle North Korea's nuclear programme.
Both US and North Korean officials discussed what full denuclearization would mean at the high-level talks, he said.
North Korean state-run news agency KCNA released a statement saying the U.S.is "fatally mistaken" if officials believe the country would follow through with aggressive demands to denuclearize the Korean Peninsula.
"We still cherish our good faith in President Trump", the spokesman said. Kim Yong Chol ended Pompeo's visit on a positive note, telling the top United States diplomat just before he boarded his plane, "We will produce an outcome, results".
"There will be things that take place along the way that help achieve the security assurances that the North Koreans need".
And Pompeo was adamant that those further negotiations would go ahead.
Despite Pompeo's positive depiction of the events, signs had emerged that things weren't going as well as hoped.
According to US media reports, Pompeo did not meet Kim during the visit, unlike his previous trips during which he had met with the DPRK's top leader.
Pompeo did not meet with Kim during his trip, but spoke far more optimistically of the talks, saying earlier Saturday "we made progress in every element of our discussions".
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There were also discussions about shutting down a missile engine testing site in the North, something President Donald Trump had said the North promised to do so before.
The top USA diplomat said Saturday the two sides "laid out a path for further negotiation" among lower-ranking officials.
Prior to North Korea's comments this afternoon, Pompeo had said: "These are complicated issues but we made progress on nearly all of the central issues". The US has insisted that North Korea give up its nuclear weapons for good before receiving relief from sanctions.
This vision will not shock seasoned North Korea-watchers, who say that Pyongyang has been largely consistent on the nuclear issue over the years.
In practical terms, Pompeo said only that officials from both sides would meet on July 12 as a working group to discuss the repatriation of the remains of some U.S. soldiers killed during the 1950-1953 Korean War.
"There will be a verification connected to the complete denuclearisation, it's what President Trump and Chairman Kim both agreed to", he added.
It would be worse for Trump himself. "It's a very, very unrealistic plan", Sue Mi Terry, Korea an analyst for the Center for Strategic and International Studies and former Central Intelligence Agency analyst, told Morning Edition on Friday, adding that just the process of verifying the full scope of North Korea's nuclear program "takes years, decades".
Doubts surfaced soon after the summit with satellite images showing continued work on North Korea's nuclear facilities and missile factories.
Despite the reports, State Department spokeswoman Heather Nauert told NBC News on Saturday that Pompeo did not deliver a CD from Trump with John's song on it. Nauert didn't immediately respond to a request for comment about North Korea's latest statement.
The secretary has come under increasing pressure to produce results, with Trump having touted the summit as a game-changing moment that eliminated North Korea's nuclear threat. "The road ahead will be hard and challenging and we know that critics will try to minimise the work that we've achieved".
Before arriving in North Korea, Pompeo said he was seeking to "fill in" some details on North Korea's commitments and maintain the momentum toward implementing the agreement from the summit. In practical terms, however, he only mentioned that officials from both sides would meet on July 12 as a working group to discuss the repatriation of the remains of some USA soldiers killed during the 1950-1953 Korean War.
CVID stands for complete, verifiable and irreversible dismantlement of the North's nuclear program, an oft-cited demand by Washington for Pyongyang.
Kim asked Pompeo if had slept well, to which Pompeo said he had.