North Korean leader Kim Jong Un's prolonged public absence has led to rumors of ill health and worries about how it could influence the future of U.S.-North Korean relations.

At Monday afternoon's White House press conference, President Donald Trump was asked if he knows what Kim's current health status is. 

Trump said, "I can't tell you exactly. Yes, I do have a very good idea, but I can't talk about it now. I just wish him well, I've had a very good relationship with Kim Jong Un." 

Trump touted his efforts to bring the two countries to a better place diplomatically saying, "If I weren't president, you'd be in war. You would have been in war with Korea. You would have been in war with North Korea if I weren't president, that I can tell you. He expected that, that I can tell you."

While the president didn't confirm details, Trump said, "I hope he's fine. I do know how he's doing relatively speaking. We will see. You'll probably be hearing in the not too distant future." 

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The rumors of Kim's ill health after his prolonged public absence has led to worries about how it could impact the future of what one analyst calls Northeast Asia's “Achilles’ heel,” a reference to the North's belligerence and unpredictable nature. 

“Instead of just saying he’s fine ... our government should prepare for various chaotic scenarios,” said Nam Sung-wook, a North Korea expert at Seoul’s Korea University. 

The exact state of Kim's health matters because it could determine the stability of the dynastic government in Pyongyang and the security of nuclear weapons that the nation has repeatedly threatened to use on its neighbors and the United States.

The Associated Press contributed to this report.