Pyongyang on Saturday staged a new ballistic missile test, but the projectile apparently exploded just minutes after being launched, according to South Korean and USA military sources.
Despite overseeing a failed missile blast on Saturday, President Trump said Kim Jong-un is a "pretty smart cookie" who will eventually build a better delivery system.
But, speaking to CBS, Mr Trump said that Mr Kim must be a "pretty smart cookie" to keep hold of power in his country. "He's dealing with obviously very tough people", Trump said.
When pressed on his reaction to another nuclear missile test, Trump said: "I would not be happy". He said North Korea poses "a grave threat", not just to the USA and its Asian allies, but also to China.
"There is a chance that we could end up having a major, major conflict with North Korea".
The United States has deployed a naval strike group to the area led by the carrier USS Carl Vinson, which on Saturday began drilling with the South Korean navy to practice procedures for tracking and intercepting enemy ballistic missiles.
North Korea is seeking to develop a long-range missile capable of hitting the United States mainland with a nuclear warhead.
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"I'd rather not discuss it, " he said. "But eventually, he'll have good missiles".
Japanese media said the destroyer is set to escort the U.S. supply ship in the Pacific Ocean south of Tokyo later on Monday in the first such operation since it passed controversial security laws allowing Japan's military a greater role in overseas activity.
Despite that, Trump said he would be "honoured" to meet the North's young leader.
The former business tycoon said: "People are saying, 'Is he sane?' I have no idea". But when asked by host John Dickerson if he would consider military action in response to another nuclear test, Trump responded: "I don't know".
That means, he said, working with partners in the region and globally on enforcing current United Nations sanctions and perhaps "ratcheting up those sanctions even further". He stressed he would not broadcast military action in order to preserve the element of surprise.
"This was a small missile", Trump said, referring to North Korea's recent failed missile test. -South Korean military drills, "U.S. aggression hysteria" reached its highest point and the situation on the Korean peninsula inched closer "to the brink of nuclear war".
Residents in the village of Seongj, where the system is being installed, scuffled with police on Sunday.