Pompeo, speaking at a counter-terrorism summit in Buenos Aires, also repeated an offer from President Donald Trump for talks without preconditions.
U.S.-Iran tensions have risen since Trump last year abandoned a nuclear deal under which Tehran agreed to curtail its nuclear program in return for the lifting of global sanctions crippling its economy.
In the latest episode to rattle nerves, Iran on Friday denied a claim by Trump that the U.S. Navy had destroyed one of its drones in the Strait of Hormuz, amid rising concern both sides could blunder into a war in the Gulf.
Pompeo reaffirmed in Buenos Aires that the drone had been brought down, despite denials from Iran, including from Foreign Minister Mohammad Javad Zarif who has said he was not aware of any downing of an Iranian drone in the strategic waterway.
(Production: Horacio Soria, Juan Bustamante)