His comments came after a Washington Post report, citing US intelligence officials, said Pyongyang had produced a nuclear warhead small enough to fit inside its missiles.
This would mean the North is developing nuclear weapons capable of striking the US at a much faster rate than expected.
The UN recently approved further economic sanctions against the country.
The Security Council unanimously agreed to ban North Korean exports and limit investments, prompting fury from North Korea and a vow to make the "US pay a price".
The heated rhetoric between the two leaders intensified after Pyongyang tested two intercontinental ballistic missiles in July, claiming it now had the ability to hit the US.
Mr Trump told reporters on Tuesday: "North Korea best not make any more threats to the US. They will be met with fire and fury like the world has never seen."
Trump threatens 'fury' against N Korea
- - Aug 09, 2017
US President Donald Trump says North Korea "will be met with fire and fury" if it threatens the US.