Recording artist Sir Elton John attends the 60th Annual Grammy Awards at Madison Square Garden on Jan. 28, 2018, in New York City. (Christopher Polk/Getty Images For Naras)

President Trump said Tuesday that he does, in fact, plan to give North Korean leader Kim Jong Un a CD with the Elton John hit “Rocket Man,” as well as another mystery gift “at a certain period.”

Trump’s remarks, which he made in a brief exchange with reporters before departing on a week-long trip to Europe, follow a report last week by a South Korean newspaper that Trump had asked Secretary of State Mike Pompeo to deliver a copy of the CD to Kim during a trip to Pyongyang last week.

“I have it for him. They didn’t give it,” Trump told reporters when asked about the CD. “But it will be given at a certain period — I actually do, I actually do have a little gift for him, but you’ll find out what that gift is when I give it.”

A representative for John did not immediately respond to a request for comment.

State Department spokeswoman Heather Nauert told reporters in Tokyo on Saturday that the only thing Pompeo left behind in Pyongyang was a letter from Trump to Kim.

Pompeo himself reportedly laughed when asked about the CD last week but did not confirm or deny the South Korean newspaper report.

“Rocket Man” is the name of a song on John’s 1972 album “Honky Château.” Trump has used “Rocket Man” as a nickname for Kim beginning last year, in a mocking reference to North Korea’s frequent missile tests. Since Kim took power in 2011, the isolated country has tested more than 85 missiles and four nuclear weapons.

Trump did not give any sense of when he might give the CD to Kim. The two held a historic summit in Singapore on June 12. Given the harsh statements from Pyongyang following Pompeo’s trip last week — the North Korean Foreign Ministry blasted Washington’s stance on denuclearization as “gangster-like” — it’s possible that it’s gonna be a long, long time.

Adam Taylor contributed to this report.