"We talked about what the North Koreans are continuing to do and how it's the case that we can get our arms around achieving what Chairman Kim and President Trump both agreed to, which is the complete denuclearisation of North Korea", Pompeo said.
"The road ahead will be hard and challenging and we know that critics will try to minimise the work that we've achieved".
The discoveries have further undercut Trump's assertion that North Korea was "no longer a nuclear threat".
The North Korean leader says he is committed to denuclearisation, but how this will be achieved is unclear.
After two days of talks with senior officials, he said efforts to push Pyongyang towards abandoning nuclear weapons had global backing.
Pompeo claimed there was "progress on nearly all of the central issues" in nine hours of "productive conversations" with Kim's right-hand man Kim Yong-chol and others but came away without any concrete agreement on denuclearization.
North Korea's angry reaction to the talks with Pompeo came in a Foreign Ministry statement that berated the Secretary over his "unilateral and gangster-like" demands and for offering no constructive steps on the U.S. side. Kim, who previously held the position of Special Envoy for North Korea Policy, met with his North Korean counterparts Sunday in Panmunjom in the Demilitarized Zone between North and South Korea shortly before Pompeo's trip. Trump offered security guarantees to Pyongyang and pledged to suspend the large-scale military drills with South Korea.
The conflicting reports come at a tense time for North Korean-U.S. relations.
Gary Neville's World Cup predictions are very impressive in hindsight
How they're still held and revered", he said, adding: "I've met quite a few of those players and we know exactly how they're held. After years of lamenting the behavior of its traveling fans, maybe now it is time for England to take more of an inward look.
Japan's Abe had praised Pompeo for his strong leadership on the issue after speaking with the Secretary of State Sunday.
U.S. State Department spokesperson Heather Nauert tweeted that Pompeo spoke briefly before leaving Pyongyang.
US Secretary of State Mike Pompeo (R) and Kim Yong Chol (L). "It can be your miracle in North Korea as well", Pompeo said.
US Secretary of State Mike Pompeo. "His dealings with North Korea have been a master class in self-deception".
"There's no doubt in my mind that it's the Chinese pulling a North Koreans back", Graham said.
In criticizing the talks with Pompeo, however, it carefully avoided attacking Trump personally, saying "we wholly maintain our trust toward President Trump, ' but stressed that Washington must not allow 'headwinds" against the 'wills of the leaders'.
Following the agreement signed at the Singapore summit, it appears that again North Korea and the USA have only committed to broad strokes and say that now the hard work is beginning, NPR's Seoul correspondent Elise Hu tells Weekend Edition Saturday. The censure was a stark contrast to the Pompeo's description of the talks as "productive".
"We thought that the United States side would come with a constructive proposal".
"North Korea's response falls short of expectation from the worldwide community... if they continue to refuse to talk about a detailed roadmap for denuclearization, doubts will grow more on their denuclearization pledge", said Chung Seong-jang, a senior researcher at the Sejong Institute. "But the economic sanctions are a different kettle of fish altogether", Pompeo said.
"We agreed to the denuclearisation of North Korea", he wrote, despite the fact that the declaration signed by the two leaders refers to the denuclearisation of the "Korean peninsula" - a vague formula that leaves room for various interpretations.