His rosy outlook was nearly immediately rejected by North Korea's foreign ministry, which called the US attitude to the talks "regrettable" and accused the United States of making unilateral demands for denuclearization.
The Trump-Kim summit in Singapore was roundly criticized by experts because it failed to nail down concrete steps or a time line to have the North abandon all its nuclear weapons and ballistic missile programs, and because the two leaders merely agreed to work toward the "denuclearization of the Korean Peninsula".
Republican Senator Lindsey Graham said on Sunday that the setback in talks between the United States and North Korea could be blamed on China. And, he and other US officials said the two countries, still technically at war after the 1950-53 Korean War, had set up working groups to deal with details of an agreement.
On Sunday, during their 40-minute trilateral meeting, Pompeo briefed Kono and Kang about the results of his latest talks with the North, Kang said.
He noted, however, that "there are things that I have to clarify", Reuters reported.
"Particularly, they have suggested that they are disappointed by the USA insistence on focusing on the denuclearisation plans over what they described as big-picture issues", she said.
Those include the formation of a working group to determine exactly how North Korea's denuclearisation will be verified and a Thursday meeting with Pentagon officials to discuss the return of remains of American soldiers killed during the Korean War.
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Earlier in the day, Prime Minister Shinzo Abe stressed the importance of a comprehensive resolution of issues related to North Korea during his meeting with Pompeo.
Following two days of diplomatic talks in North Korea, Pompeo told reporters this morning that "a good deal of time" had been spent discussing a timeline for slowing down nuclear ambitions. "The choice now lies with North Korea and its people".
Before departing for Japan, Pompeo briefly addressed the meetings with North Korea, saying, "Some places [there was] a great deal of progress; other places there's still more work to be done".
"I know my counterpart [Kim Yong-choi] spoke with Chairman Kim during the course of our negotiations as well".
"The commitment that Chairman Kim made is important and powerful, and I am convinced that he understands the commitment he made, and I am hopeful that we will find a path forward to achieve that commitment that Chairman Kim himself made personally to President Trump and then to [the] world in the signed agreement between our two leaders", Pompeo added.
However, the president has since renewed sanctions on North Korea, while United States intelligence officials have said there is evidence North Korea continues to upgrade the infrastructure for its nuclear and missile programmes.
It was Mr Pompeo's first visit to the North since last month's summit between Kim Jong-un and President Donald Trump. North Korea committed at last month's summit to the "immediate repatriation" of remains already identified, but that hasn't happened yet.
However, Pompeo said the progress achieved thus far did not warrant any concessions. "We pushed them really hard to live up to the commitments of the president, and they may be reacting to save face", a source, who asked not to be named, told ABC News.