The US has warned the North Korean regime that it would be "utterly destroyed" if war were to break out.
Hours after the isolated state's latest ballistic missile test, the US ambassador to the UN urged all countries to cut diplomatic and trade ties with Pyongyang.
At an emergency meeting of the UN Security Council, Nikki Haley said: "We have never sought war with North Korea, and still today we do not seek it.
"If war does come, it will be because of continued acts of aggression like we witnessed yesterday.
"And if war comes, make no mistake, the North Korean regime will be utterly destroyed."
The missile was claimed by North Korea to be its most powerful so far and to be capable of reaching the US mainland.
In September, North Korea also tested its sixth, and largest, nuclear bomb - part of a programme which it says is based on its need for self-defence.
The US and South Korea are due to hold military exercise in December.
Donald Trump's administration had said all options were on the table when it came to dealing with the ballistic and nuclear weapons programmes but it preferred diplomacy.
But the President has resorted to name calling at times, describing North Korean leader Kim Jong Un as "Little Rocket Man" and a "sick puppy" during a speech in Missouri on Wednesday.
Mr Kim, for his part, has called Mr Trump "frightened dog" and a "gangster fond of playing with fire".
On Wednesday, Mr Trump wrote on Twitter that he had talked with President Xi Jinping of China about "additional major sanctions" against North Korea.
Ms Haley said that the US had asked China to cut its supply of oil to the communist nation.
Relying on China to use its influence over the North Korean dictatorship is a strategy that Mr Trump has often promoted, but it seems to have done little to calm the tensions so far.
China's deputy UN ambassador Wu Haitao described the current situation as "grave" but called for all parties to exercise restraint, implement UN sanctions and "strive for the early resumption of dialogue and negotiations".
Speaking at the same meeting as Ms Haley, he said he hoped a China-Russia idea that would see North Korea suspend testing in exchange for the US and South Korea suspending military exercises would "elicit a response and support".
Russia's UN ambassador Vassily Nebenzia said his country was "deeply disappointed" with North Korea's missile launch, calling on all parties to stop the "spiral of tension".
North Korea has said its missile earlier this week reached a height of 4,475 km and flew 950 km during the 53 minutes it was in the air.