Earlier Pyongyang said it was ready to give Washington a "severe lesson" with its strategic nuclear force in response to any US military action.
Washington has warned it is ready to use force if need be to stop North Korea's weapons ballistic missile and nuclear programs but has said it prefers global diplomatic action, including sanctions.
The consequences of a US strike would potentially be catastrophic for South Koreans, Japanese and US military personnel within range of North Korean retaliatory strikes.
"North Korea best not make any more threats to the United States. They will be met with fire and fury like the world has never seen," Trump told reporters at the Trump National Golf Club in Bedminster, New Jersey.
Earlier on Tuesday, Japan's Defence Ministry said "It is conceivable that North Korea's nuclear weapons programme has already considerably advanced and it is possible that North Korea has already achieved the miniaturisation of nuclear weapons and has acquired nuclear warheads."
The UN Security Council unanimously imposed new sanctions on North Korea on Saturday over its continued missile tests that could slash the reclusive country's $3 billion annual export revenue by a third.
North Korea said the sanctions infringed its sovereignty and it was ready to give Washington a "severe lesson" with its strategic nuclear force in response to any US military action.
North Korea has made no secret of its plans to develop a nuclear-tipped missile capable of striking the United States and has ignored international calls to halt its nuclear and missile programmes.
North Korea says its intercontinental ballistic missiles (ICBMs) are a legitimate means of defence against perceived US hostility. It has long accused the United States and South Korea of escalating tensions by conducting military drills.
US stocks fell, with the S&P 500 at a session low after Trump's comment, while a widely followed measure of stock market anxiety spiked higher and was on track to close at a one-month high. The US dollar index slightly pared gains as the safe-haven yen strengthened against the US currency.