The statement said the United States betrayed the spirit of last month's summit between President Donald Trump and North Korean leader Kim Jong Un by making unilateral demands on "CVID", or the complete, verifiable and irreversible denuclearization of North Korea.
In practical terms, Pompeo mentioned 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.
Meanwhile, North Korea says it disagrees with the USA calls for denuclearization, and called the discussions with Pompeo very concerning.
It was the first time he had visited North Korea since the Donald Trump-Kim Jong-un summit in Singapore.
"But through the high-level talks, the trust between the DPRK and the United States is facing a risky situation where our resolve for denuclearisation, which has been firm and steadfast, may falter".
Mr Pompeo said that North Korea, in the "many hours of talks" at a walled-off guesthouse outside downtown Pyongyang, reiterated its commitment to denuclearisation.
"I know my counterpart [Kim Yong-choi] spoke with Chairman Kim during the course of our negotiations as well".
Pompeo's talks will be closely watched in the region. Pompeo asserted that the United States will again meet with North Korea next week in the demilitarized zone. Trump has declared on Twitter that North Korea no longer poses a nuclear threat.
Out of the talks, a meeting has been arranged for July 12 at the Korean demilitarized zone to discuss with North Korean officials the return of USA service members remains, according to Pompeo, who said that the date could move "by one day or two".
"But, the US side came up only with its unilateral and gangster-like demand for denuclearisation just calling for CVID, declaration and verification".
Kim Yong Chol asked Pompeo if he had slept well on his first overnight stay in the country, adding: "But we did have very serious discussion on very important matters yesterday".
Mr Pompeo and Kim Yong Chol met for almost three hours on Friday and then had dinner amid growing scepticism over how serious Kim Jong-un is about giving up his nuclear arsenal and translating the upbeat rhetoric following his June 12 summit with Trump into concrete action.
"I think we've made progress in every element of our discussion", he said, describing the conversations as "productive, good faith negotiations".
Doubts surfaced soon after the summit with satellite images showing continued work on North Korea's nuclear facilities and missile factories.
The alleged gift came after the song became a point of discussion for Trump and Kim during their summit in Singapore last month.
A meeting between Mr Pompeo and Kim Jong-un later on Saturday was expected but not certain, U.S. officials said.
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