But, speaking to CBS, Mr Trump said that Mr Kim must be a “pretty smart cookie” to keep hold of power in his country.
“People are saying, ‘Is he sane?’ I have no idea…. but he was a young man of 26 or 27… when his father died. He’s dealing with obviously very tough people, in particular the generals and others.
”And at a very young age, he was able to assume power. A lot of people, I’m sure, tried to take that power away, whether it was his uncle or anybody else. And he was able to do it. So obviously, he’s a pretty smart cookie,“ Mr Trump said.
The comments come after North Korea launched a mid-range ballistic missile on Saturday, which broke up a few minutes after launch, the third test-fire that failed in April. The programme’s repeated failures over the past few years have given rise to suspicions of US sabotage.
In pictures: North Korea military drill
In the interview with Face the Nation, the President was asked why North Korea’s rockets keep blowing up.
“I’d rather not discuss it,” Mr Trump said. “But perhaps they’re just not very good missiles. But eventually, he’ll have good missiles.”
He added: “And if that happens, we can’t allow it to happen.”
North Korean ballistic missile tests are banned by the United Nations because they are seen as part of the North’s push for a nuclear-tipped weapon that can hit the US mainland. North Korea’s regional neighbours South Korea, China and Japan are also on high alert.
Elsewhere, Mr Trump’s National Security Adviser, Lt. Gen. HR McMaster said that Trump “has made clear that he is going to resolve this issue one way or the other,” but that the President’s preference is to work with China and others to resolve it without military action.
That means, Lt. Gen. McMaster said, working to enforce current UN sanctions and perhaps ratcheting them up. “And it also means being prepared for military operations if necessary,” he added.
The blitz of television coverage comes amid weeks of escalating tensions over the actions of North Korea, with the Trump administration never decisively saying that military action would be forthcoming.
When asked, Mr Trump said Mr Kim will eventually develop better missiles, and “we can’t allow it to happen.”
But, the President would not discuss the possibility of military action – saying “I don’t know…we’ll see” when asked if another missile launch by North Korea would mean retaliation. He added: “It is a chess game. I just don’t want people to know what my thinking is.”
Agencies contributed to this report