Pompeo and Kim met during the secretary of state's two trips to Pyongyang in April and May.
Gen Kim's visit to the United States will be the most high-profile visit by a member of the North Korean regime since top military official Jo Myong-rok travelled to Washington in 2000, where he met President Bill Clinton and became the first North Korean officer to enter the Pentagon.
When Kim Yong Chol lands in NY this week, he will become the most senior North Korean envoy to hold talks with American officials on USA soil in 18 years.
Rapid-fire diplomacy played out on two continents Tuesday in advance of an "expected" summit between President Donald Trump and North Korea's Kim Jong Un, the strengthening resolve coming after a series of high-risk, high-reward gambits by the two leaders.
Nauert provided no further details.
A senior North Korean official is headed to NY to discuss an upcoming summit, US President Donald Trump says, the latest indication that an on-again-off-again meeting between Mr Trump and North Korea's leader may go ahead next month.
Sung, a South Korean born diplomat, is a former nuclear negotiator and current USA ambassador to the Philippines. It includes senior officials with the National Security Council and the Pentagon. It is reported by Japanese TV channel TBS.
At the same time, a "pre-advance" USA team was in Singapore to meet North Koreans.
Trump confirmed Tuesday that Kim was to hold talks with Secretary of State Mike Pompeo.
The historic meeting is scheduled to take place in Singapore on June 12.
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Speaking on the matter, President Moon says, "If we could hold working-level, back-to-back talks on both sides of Panmunjom if urgently necessary in addition to formal summits, it would expedite faster advancement of inter-Korean relations".
The Washington Post said the meetings would continue on Monday and Tuesday at Tongilgak, the North's building in Panmunjom, where the truce suspending the 1950-53 Korean War was signed. "In some ways, Kim Jong Un may have met his match here with our very unconventional president". "What's unclear for Chairman Kim, in my opinion, is not his willingness for denuclearization but whether he can certainly trust the USA saying that it'll end hostile relations and guarantee the security of his regime after his denuclearization".
A "pre-advance" team of US officials has also traveled to Singapore to meet with North Koreans there, the White House said.
A USA official told Reuters that Sung Kim, the former US ambassador to South Korea and current ambassador to the Philippines, was leading the American delegation to meet North Korean officials at the border. Last week, Trump withdrew from the meeting, only to announce a day later it could still get back on track.
Moon and Kim held unannounced talks on Saturday in the DMZ. "They make him feel prestigious, they make him feel powerful". Experts point to countries resistant to the US sanctions as helping keep Kim's $40 billion economy going, the Journal reported. Libyan dictator Moammar Qaddafi was killed in an uprising several years later.
But South Korea, which has lobbied hard for the talks between Trump and Kim, has insisted that Kim can be persuaded to abandon his nuclear facilities, materials and bombs in a verifiable and irreversible way if offered credible security and economic guarantees. "We believe that it is necessary to establish a hotline between North Korea and the United States", Moon said at a press conference on Sunday.
Trump announced that Kim Yong Chol was coming to NY for talks with Pompeo in a tweet on Tuesday in which he said he had a "great team" working on the summit.
But with only a few weeks left until the scheduled summit, such talks appear unlikely to reconcile the differing positions over Pyongyang's nuclear arsenal, he said.
Kim "has nearly an emotional attachment and a personal psychological attachment to these nuclear weapons", US Senator Marco Rubio said Sunday on ABC's "This Week".
"I remain convinced that he does not want to denuclearize, in fact he will not denuclearize", Rubio, a member of the Senate Foreign Relations and Intelligence committees.