Before arriving, he also said in a tweet that he hoped to achieve North Korea's "final, fully verified denuclearisation" - raising questions whether the administration had softened its longstanding goal of "complete, verifiable and irreversible denuclearisation".
The North's spokesman said: "We expected that the US side would come with productive measures conducive to building trust in line with the spirit of the North-US summit and (we) considered providing something that would correspond to them".
North Korea, however, said the "attitude" of the United States was "regrettable" and not in the spirit of the June 12 summit in Singapore between President Donald Trump and North Korean leader Kim Jong Un.
However, the spokesman said the U.S. had come up with a variety of "conditions and excuses" to delay a declaration on ending the war.
"But, the US side came up only with its unilateral and gangster-like demand for denuclearisation just calling for CVID, declaration and verification".
"The high-level talks this time brought us in a risky situation where we may be shaken in our unshakable will for denuclearisation, rather than consolidating trust between the DPRK and the U.S". The State Department said its policy remains unchanged. They said the United States was not following the spirit of the Kim-Trump summit, and was just making demands throughout Pompeo's visit.
The secretary of state said, he spent "a good deal of time" talking about a denuclearization timeline and missile facilities. "These are complicated issues but we made progress on nearly all the central issues".
"Some places, [we've made] a great deal of progress", Pompeo said. The North Korean delegation was led by Kim Yong-chol, a senior aide to the country's leader.
Following last month's summit in Singapore, senior US and North Korean diplomats struggled to maintain basic communication, leading to concerns that the talks would require Pompeo, who has many other responsibilities, to devote an unmanageable amount of time on the Korea issue.
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Both goalkeepers made early saves in the shootout, with an injured Danijel Subasic stopping the opening shot from Fyodor Smolov. And in the extra session, it looked like Croatia was well on their way to the victory and avoiding penalty kicks.
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They return to action on Wednesday when they meet England (19:00 BST) in Moscow for a place in the final on 15 July. Many fans gave him a standing ovation when he was taken off in the second half.
Senior North Korea official Kim Yong Chol agreed with Pompeo's remarks, adding that there were areas which Pyongyang needed to shed light on. There is no sign that Kim Jong Un is contemplating what nuclear experts say has to be the first step: a full disclosure of his weapons program, to create a baseline for future inspection and verification, fundamental to any arms-control agreement. Trump's impulsive acceptance of the first summit between a North Korean leader and an American president was always going to be largely ceremonial.
Meanwhile, North Korea says it disagrees with the USA calls for denuclearization, and called the discussions with Pompeo very concerning.
A state department spokesperson said Mr Pompeo had been "very firm" in focusing on denuclearisation, as well as on security assurances and another important USA demand - the return of remains of U.S. service personnel from the Korean War.
He also said Pentagon officials will meet with their North Korean counterparts on or near July 12 at the demilitarized zone between the Koreas to discuss the return of USA military personnel who died during the Korean War.
The issue of the remains of USA soldiers missing from the Korean War is also high on the agenda.
"Nothing could be further from the truth", State Department spokesperson Heather Nauert said in response.
The bombshell threat came just momebnts after Mr Pompeo hailed progress in Pyongyang on setting a timeline to North Korea's denuclearisation. That depends on which translation you prefer of North Korea's statement.
The top U.S. diplomat has said that Kim had repeatedly expressed in private conversations his desire to give up nuclear weapons for good. North Korea committed at last month's summit to the "immediate repatriation" of remains already identified, but that hasn't happened yet.