They were due to talk again all day Saturday before Pompeo heads to Tokyo to brief Washington's Japanese and South Korean allies.
'The road ahead will be hard and challenging and we know critics will try to minimize what we have achieved, ' he said.
"These are complicated issues but we made progress on nearly all the central issues", the Secretary of State said.
"We thought that the U.S. side would come with a constructive proposal which accords with the spirit of the DPRK-U.S. summit meeting and talks. I am determined to achieve the commitment that President Trump made and I am counting on Chairman Kim to be determined to follow through on the commitment that he made", Pompeo said.
The leader's meeting ended with a promise from Mr Kim to work towards denuclearisation, but details on how this will be achieved remain thin.
Pompeo shrugged off the statement Sunday following separate meetings with the foreign ministers of Japan and South Korea - although he didn't disagree with the nature of the U.S.'s "gangster-like" requests.
Leaked US intelligence findings concluded that North Korea does not intend to give up its nuclear programme completely.
"I know my counterpart [Kim Yong-choi] spoke with Chairman Kim during the course of our negotiations as well".
"And to our North Korean friends, I can't say the word friend yet". In June, President Trump falsely claimed that the repatriation was already in the works.
"But a rushed summit and demands that NK denuclearize in short order or else is not a serious test of diplomacy", Haass tweeted.
He said North Korea had confirmed it meant to destroy a missile-engine testing facility and the two sides discussed the "modalities" of what that would look like.
He added that he believes it was a "mistake" for Trump to agree to call off military exercises with South Korea amid ongoing discussions with the North. "At the same time we have reaffirmed that the global community will continue to fully implement relevant U.N. Security Council resolutions", Kono said.
Japanese Prime Minister Shinzo Abe earlier at his residence in Tokyo praised Pompeo. 'If I paid attention to the press, I'd go nuts'.
After the historic U.S.
'Dealing with North Korea is hard because Kim Jong Un wants it to be hard, ' said Russel, who was assistant secretary of state for East Asian and Pacific Affairs in the Obama administration.
But, the statement continued, "The attitude and position of the US during the talks. was regrettable". "We had productive, good-faith negotiations".
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.
The talks are part of a broader USA initiative to persuade North Korea to give up its nuclear and ballistic missile programs.
"We now have a meeting set up for July 12 - it could move by one day or two - where there will be discussions between the folks responsible for the repatriation of remains".
It dismissed Trump's unilateral order to suspend joint USA and South Korean war games as a cosmetic and "highly reversible" measure and criticised U.S. negotiators who "never mentioned" the subject of bringing the 1953 Korean War to a formal end with a peace treaty.
"The U.S. side came up only with its unilateral and gangster-like demand for denuclearization", the statement, shared by The Post, said.
There had also been worrying signs even before the Pompeo trip.
Some U.S. experts said the disputes highlight the risk of Trump granting premature concessions to North Korea.