Kim shot back at Trump on Thursday, describing him as "mentally deranged" and warning he would "pay dearly" for his threat.
Trump had warned the North Korean leader in his UN address on Tuesday that the United States, if threatened, would "totally destroy" the country of 26 million people and mocked Kim as a "rocket man" on a suicide mission.
Russian Federation and China are pushing a joint proposal to kick-start talks with North Korea by freezing Pyongyang's nuclear and missile tests in exchange for a suspension of US-South Korean military drills.
The bellicose speech came after months of escalating tensions over advances in the rogue weapons programme operated by Pyongyang, which has defied tough sanctions to launch its sixth and largest nuclear test and to fire a series of missiles over Japan.
"This mission is a demonstration of USA resolve and a clear message that the president has many military options to defeat any threat", Ms White said.
Trump also announced the order gives the United States government discretion to sanction foreign banks that conduct transactions tied to trade with the North.
For reference, the US agency recorded a 6.3 magnitude quake after North Korea's hydrogen bomb test on September 3, its sixth of a nuclear weapon.
Until now, the North has not tested its missiles and nuclear weapons together, opting instead to fire them separately - the missiles above ground and the nuclear weapons below.
"We have no idea about what actions could be taken as it will be ordered by leader Kim Jong Un".
In recent months, North Korea has launched a pair of intercontinental missiles believed capable of striking the continental USA and another pair that soared over Japanese territory.
The US president's move to punish foreign companies that deal with the North was the latest salvo in a US-led campaign to isolate and impoverish Kim's government until his country halts its missile and nuclear tests.
A secondary tremor detected after that test could have been caused by the collapse of a tunnel at the mountainous site, experts said at the time.
"We see it not just in this arena, interfering with democratic processes, we see it in advancing the face of terrorism around the world", he said.
Muir said. "Will there be military action?"
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