US Defence Secretary James Mattis has said North Korea should cease any consideration of actions that would "lead to the end of its regime and the destruction of its people".
Mr Mattis said any action by North Korea would be grossly overmatched by the US, and that Pyongyang would lose any arms race or conflict it started. He said that while the US is pursuing diplomatic solutions, the combined military power of America and its allies is the most robust on Earth.
Mr Mattis issued a statement as he travelled to the West Coast. His comments punctuate President Donald Trump's warning that North Korea will be met with "fire and fury" if it threatens the US.
A new report says Pyongyang's nuclear programme is progressing.
Meanwhile, France is urging all sides "to act responsibly and to de-escalate" tensions over North Korea's nuclear ambitions.
French government spokesman Christophe Castaner said Paris is "watching what's going on with concern" and "is ready to put all its means at disposal so we can find a peaceful solution".
Britain's UN ambassador said the United Kingdom "stands shoulder to shoulder with the United States" in tackling the nuclear threat from North Korea and making sure it cannot pursue its nuclear and ballistic missile programmes.
Matthew Rycroft told reporters at UN headquarters in New York that the US and UK have been very clear in demanding a halt to North Korea's nuclear and missile programmes. He said Kim Jong Un's regime should listen to and "act on that clarity".
Mr Rycroft stressed that North Korea "holds the key to sanctions being removed".
Asked whether Mr Trump's escalating rhetoric was hurting prospects for reviving negotiations, Mr Rycroft said: "What's hurting the six-party talks is the inability so far of the North Korean regime to do what it has to do which is to halt its nuclear programme and to halt its intercontinental ballistic missile programme."