President Trump on Tuesday said he wishes Kim Jong Un well amid speculation that the North Korean leader is in declining health.

"These are reports that came out, and we don't know," Trump told reporters. "I've had a very good relationship with him. I can only say this: I wish him well because if he is in the kind of condition that the reports say, that the news is saying, that's a very serious condition, as you know."

"I've said it, and I've said it many times: If somebody else were in this position, we would've been right now at war with North Korea," Trump added, repeating a frequent but unproven claim about his diplomacy with Kim.

Multiple news outlets reported late Monday that Kim was in grave condition following an undisclosed surgery earlier in the month. But South Korea's government said there was no indication of any issues from North Korea, sparking uncertainty about the reclusive Kim's status.

National security adviser Robert O'Brien said Tuesday morning that the U.S. is "keeping a close eye" on reports about Kim's health but would not elaborate on reports about his condition.

"We're monitoring these reports very closely," O'Brien told the hosts of "Fox & Friends," adding that North Korea "is a very closed society. There's not a free press there. They're parsimonious with the information they provide about many things, including the health of Kim Jong Un."

Trump often touts his personal relationship with the North Korean leader, who has been accused of starving and torturing his own people, among other human rights violations.

Trump and Kim have held two face-to-face summits over the past two years, and Trump in June 2019 made history by becoming the first sitting U.S. president to cross into North Korea following a meeting with Kim at the Demilitarized Zone.

The president had pushed at those meetings for Kim to abandon his nuclear arsenal, but thus far the North Korean leader has not taken any steps toward doing so. The country restarted ballistic missile testing last year, drawing criticism from U.S. allies and international watchdogs.

Trump has downplayed those tests, saying he is confident in his personal relationship with Kim.