The North Korea official news agency said it was mulling a plan to fire medium-to-long-range rockets around Guam, where US strategic bombers are based.
The statement marks a sharp rise in rhetoric between the two countries.
The UN recently approved further economic sanctions against the country.
President Trump’s comments followed a media report that claimed the North had made a nuclear warhead small enough to fit inside its missiles.
The Washington Post report, which cited US intelligence officials, suggests North Korea is developing nuclear weapons capable of hitting the US at a much faster rate than expected.
The North’s official Korean Central News Agency (KCNA) said its military was “carefully examining the operational plan for making an enveloping fire at the areas around Guam with medium-to-long-range strategic ballistic rocket Hwasong-12”.
It said the plan would be reported to the Supreme Command after “full examination and completion” and put into practice at the order of leader Kim Jong-un, South Korea’s Yonhap news agency reported.
The heated rhetoric between the US and North Korea intensified after Pyongyang tested two intercontinental ballistic missiles (ICBM) 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.”
Veteran US Senator John McCain was sceptical about Mr Trump’s statement.
“The great leaders that I have seen, they don’t threaten unless they are ready to act and I’m not sure that President Trump is ready to act,” said Senator McCain.
