The comments came as White House National Security Advisor H R McMaster warned of the "increasing" possibility of war with the impoverished but nuclear-armed North.
The five-day Vigilant Ace drill -- involving some 230 aircraft including F-22 Raptor stealth jet fighters -- begins tomorrow, five days after the North test-fired an intercontinental ballistic missile believed capable of hitting the US mainland in a fresh challenge to President Donald Trump.
The North's ruling party Rodong newspaper slammed the upcoming drill.
"The US and South Korean puppet warmongers would be well advised to bear in mind that their DPRK-targeted military drill will be as foolish as an act precipitating their self- destruction," it said.
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The commentary was published a day after Pyongyang's foreign ministry accused the Trump administration of "begging for nuclear war" by staging what it called the reckless air drills.
McMaster said the possibility of war with the North was "increasing every day".
"There are ways to address this problem short of armed conflict, but it is a race because he's getting closer and closer, and there's not much time left," he said.
The North says the Hwasong-15 missile fired on Wednesday can be tipped with a "super-large heavy warhead" capable of striking the whole US mainland.
But analysts remain unconvinced that it has mastered the advanced technology to allow the rocket to survive re-entry to the Earth's atmosphere.
But even some Trump advisers say US military options are limited when Pyongyang could launch an artillery barrage on the South Korean capital Seoul -- only around 50 km from the border and home to 10 million people.