"Trump then asked Kim if he knew the song and Kim said no", the South Korean daily quoted a Washington official as saying. "These gestures alone don't ensure progress in denuclearizing the North and stabilizing peace".
"We have a pretty good understanding of what [Kim] has, including some things that he's never acknowledged to the worldwide community before", Morell said.
Trump remembered the conversation and told Pompeo to take a CD with the song for Kim.
"So far principal results of Singapore summit have been to sow doubts about U.S. commitment to its South Korean ally, to weaken sanctions on NK, and to raise questions about U.S. seriousness given enormous gap between rhetoric of denuclearization and reality", tweeted Richard Haas, president of the Council on Foreign Relations and a top foreign policy adviser to both Presidents Bush.
He will spend the night in the North Korean capital, marking his first overnight stay in the country.
"It feels like the first time I came here all over again, " said Hur Jae, head coach of South Korea's men's national team, who previously visited Pyongyang for a joint game in 2003.
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He last visited in May ahead of the Trump-Kim summit and traveled there secretly in early April while he was director of the Central Intelligence Agency.
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In a statement Thursday, South Korea's Foreign Ministry said Foreign Minister Kang Kyung-wha will meet with Pompeo and his Japanese counterpart, Foreign Minister Taro Kono.
North Korea has consistently refused in past rounds of failed negotiations to provide an inventory of its weapons program, and USA intelligence remains uncertain of how many nuclear warheads North Korea has. Although the North agreed to return their remains, details need to be ironed out, and North Korea has not yet taken delivery of some 100 coffins that are waiting at the border.
Pomepo said yes and added, "I'm looking forward to our time together today".
Trump needs Pompeo to score some points to lay to rest doubts over whether the president, who has already ordered a suspension of large-scale US military drills with South Korea, is hurting the bigger goal of complete denuclearization by being overeager to claim a quick success.
This will be Pompeo's third trip to North Korea in three months. The regime vowed to obtain a submarine capable of launching a long-range ballistic missile before the Trump-Kim summit.
Defense Secretary Jim Mattis said last month that the United Nations command in South Korea would initially take charge of the transfer of remains - when they occur - and would then turn them over to the custody of the USA military.
Private analysts have been quick to pick apart the administration's overall plan for following up on the summit in Singapore, where Mr. Kim committed generally to the goal of a "complete denuclearization of the Korean Peninsula".