Rumors about the alleged unusual gift were sparked by a report in the South Korean newspaper Chosun Ilbo on Friday.
Kang In-sung, a Washington-based correspondent for the widely read conservative publication, had quoted an unnamed diplomatic source who said that Trump had signed a copy of the CD for Kim, as the North Korean leader had asked about the song during their meeting in Singapore last month.
Trump had dubbed Kim “Rocket Man” last year, in reference to repeated North Korean missile tests. Since Kim took power in 2011, the isolated country has tested more than 85 missiles and four nuclear weapons. “Rocket Man” is the name of a song on the 1972 album “Honky Château.”
Chosun Ilbo's report was widely shared — perhaps in part because it suggested a lighthearted side to tense denuclearization talks between the United States and North Korea. The story may have also suggested to some that Kim had a sense of humor about himself, despite his reputation as a totalitarian ruler.
Pompeo was asked about the CD earlier by a journalist accompanying him to North Korea; the secretary of state laughed but did not confirm or deny the report.
Nauert on Saturday told reporters that Pompeo did not meet Kim during this visit to North Korea but also that they had not expected him to. Instead, Pompeo spent most of his time in meetings with his counterpart negotiator, Kim Yong Chol, a former spy chief who had lightheartedly teased him about his sleep habits.
The talks between Pompeo and Kim Yong Chol were the first high-level, face-to-face meetings since Trump and Kim Jong Un met last month in Singapore, where they reached an agreement to work toward denuclearization of the Korean Peninsula, among other things.
Amid increasing scrutiny of North Korea's commitment to giving up its weapons, Pompeo came to Pyongyang in a bid to hammer out the details of a denuclearization plan. While the secretary told reporters that progress was made "on almost all of the central issues” and involved “good-faith negotiations,” North Korea said the U.S. attitude, demanding denuclearization, was “regrettable.”