The second trilateral meeting in less than a month followed U.S. Secretary of State Mike Pompeo's visit to Pyongyang on Friday and Saturday where he tried to work out the specifics of denuclearization with senior North Korean officials.
It was not clear if Pompeo would be granted an audience with the Northern leader himself as he tries to develop a detailed road-map towards the "complete denuclearization" of the Korean peninsula, as agreed by Kim and US President Donald Trump last month.
Kim Yong Chol said that the two had had "very serious discussion on very important matters yesterday" and joked that as a result, Pompeo "might have not slept well last night" at the prestigious Paekhwawon, or 100 Flowers Garden, guest house.
"The more we meet, the deeper our friendship will be, I hope", he said, adding: "Today's meeting is a really meaningful meeting".
"If those requests were gangster-like, the world is a gangster", Pompeo said, noting that numerous U.N. Security Council resolutions have demanded that the North rid itself of nuclear weapons and end its ballistic missile program.
Mr Pompeo said he did not meet Mr Kim on his latest visit to Pyongyang, as he had done twice before. "I am determined to achieve the commitment that President Trump made, and I'm counting on chairman Kim to be determined to follow through on the commitment that he made".
State Department spokesperson Heather Nauert on Saturday said USA and North Korean officials have established a working group to deal with the "nitty-gritty stuff", according to pool reporters accompanying Pompeo.
Nauert said Pompeo's discussions with North Korean officials also included repatriation of American Korean War remains.More news: Fortunate Forsberg helps Sweden past Swiss into World Cup quarters
Pompeo had previously offered a more optimistic view of the talks, which were held with top North Korean party official and former spy chief Kim Yong Chol. Nauert told reporters that the two sides spoke during a dinner following their almost three-hour meeting Friday night and they were "cracking jokes" and "exchanging pleasantries". Pompeo departed for Tokyo on Saturday afternoon and did not speak to Kim Jong Un on this trip as he has in the past, according to Nauert. They buy $100 billion from us.
After talks with the foreign ministers of Japan and South Korea on Sunday, the secretary of state said his efforts to press the North on nuclear weapons were legitimate.
"The miracle could be your miracle", Pompeo said of North Korea and its leader.
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.
He said the key to Vietnam's rise was post-Vietnam War engagement with the United States, which began in 1985, when the countries started working together to repatriate remains of US service members lost in Vietnam. Trump said after the Singapore summit that Kim had agreed to send the remains back to the United States.
Pompeo, however, said more talks were needed on both.
It said the North had raised the issue of formally ending the Korean War, which concluded with an armistice and not a peace treaty, but the US came up with a variety of "conditions and excuses" to delay a declaration. She cautioned Mr. Trump against considering working with Russian Federation to oust Iran from Syria in return for the US reducing its troop presence in the country. He committed to complete denuclearization.