The incident, which occurred Sunday and was first reported by Reuters, comes as U.S. President-elect Donald Trump prepares to take office on Jan. 20. In September, Trump vowed that any Iranian vessels that harass the U.S. Navy in the Gulf would be "shot out of the water."
The officials, speaking on the condition of anonymity, said the USS Mahan established radio communication with the Islamic Revolutionary Guard Corps boats but they did not respond to requests to slow down and continued asking the Mahan questions.
The Navy destroyer fired warning flares and a U.S. Navy helicopter also dropped a smoke float before the warning shots were fired.
The Iranian vessels came within 900 yards (800 meters) of the Mahan, which was escorting two other U.S. military ships, they said.