Pompeo replied: "Director Kim, I slept just fine".
'The road ahead will be hard and challenging and we know critics will try to minimize what we have achieved, ' he said.
In a statement released by an unnamed foreign ministry spokesman, Pyongyang accused the USA of betraying the spirit of last month's summit between Donald Trump and Kim by making "one-sided and robber-like" demands on "CVID" - the complete, verifiable and irreversible denuclearisation of North Korea.
Mr Pompeo also sought to dispel suggestions the Trump administration had backed down from demanding the complete, verifiable and irreversible dismantlement of the North's nuclear weapons. At the summit, Mr. Kim committed to complete denuclearization in return for us security guarantees.
Pompeo said on Twitter after he met Kono he was in Tokyo to discuss the USA alliance with Japan and maintaining "maximum pressure" on North Korea, an expression Trump's administration had backed away from after the Singapore summit.
Some U.S. experts said the disputes highlight the risk of Trump granting premature concessions to North Korea. When the two leaders met at a diplomatic summit in Singapore last month, the "Rocket Man" tag came up during friendlier talks.
"Sanctions will remain in place until final, fully verified denuclearisation as agreed to by Chairman Kim (Jong Un) occurs", Pompeo said, adding that the U.S. would seek to smooth the path by providing security guarantees requested by Pyongyang.
He added that his two days of talks with senior North Korean officials had "made progress" and included a "detailed and substantive discussion about the next steps towards a fully verified and complete denuclearisation".
"We confirmed that security assurances will be provided to North Korea as agreed in the summit".
"If those requests were gangster-like, the world is a gangster, because there was a unanimous decision at the UN Security Council about what needs to be achieved", he said.
Japanese Prime Minister Shinzo Abe earlier at his residence in Tokyo praised Pompeo.
As they began their talks on Saturday, Kim Yong Chol alluded to the fact that Pompeo and his delegation had stayed overnight in Pyongyang.
After the historic U.S.
U.S. Secretary of State Mike Pompeo on Saturday wrapped up a visit to the Democratic People's Republic of Korea (DPRK), which he said has seen some progress but the DPRK said is regrettable.
Pompeo, accompanied by senior State Department and Central Intelligence Agency officials, held nearly three hours of talks on Friday evening.
Even so, the USA envoy on Sunday insisted again that he thought the talks were "in good faith and productive".
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'.
US intelligence officials told Reuters that Pompeo would try to agree on at least an initial list of nuclear sites and an inventory that could be checked against available intelligence. "Some places a great deal of progress, other places there's still more work to be done", said Pompeo, according to a pool report from usa reporters who accompanied him to Pyongyang.
The threat comes just a few weeks after Mr Trump said a process of "total denuclearisation has already started" and that North Korea was blowing up four of its big test sites.
In practical terms, Pompeo mentioned only that officials from both sides would meet on July 12 to discuss the repatriation of the remains of some United States soldiers killed during the 1950-1953 Korean War.
KCNA said Pyongyang had offered to discuss declaring a formal end to the 1950-53 Korean War to mark next month's anniversary of the armistice agreement.
"The issues the US side insisted on at the talks are all roots of troubles, which the previous administrations also had insisted on to disrupt the dialogue processes, stoke the distrust and increase the danger of war", the statement read.
"The North Koreans are in the game to get, not to give", said Daniel Russel, the top USA diplomat for East Asia until past year. Before this trip, Pompeo said he was hoping to "fill in" some of the details on what North Korea committed to at the summit.
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