Ri Yong-ho said this could apply even if the warplanes were not in North Korea's airspace.
The White House dismissed the statement as "absurd". The Pentagon warned Pyongyang to stop provocations.
A UN spokesman said fiery talk could lead to fatal misunderstandings.
Mr Ri's comments were a response to Mr Trump's tweet that the North Korean leadership would not "be around much longer" if they continued their rhetoric.