In a statement about the incident, Chief Pentagon Spokesperson Jonathan Hoffman said a drone approached the USS Boxer at around 10 a.m. local time and that the ship was in worldwide waters, sailing in "an inbound transit of the Strait of Hormuz".
"This was the latest of many hostile and provocative actions by Iran against vessels operating in worldwide waters.", he continued.
"The U.S. reserves the right to defend personnel, facilities, interests", he said.
The president says the drone threatened the safety of the American ship and its crew.
"A fixed-wing unmanned aerial system approached Boxer and closed within a threatening range", chief Pentagon spokesman Jonathan Hoffman said in a written statement. "I also call on other nations to protect their ships as they go through the Straight of Hormuz and to work with us in the future".
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Iran recently shot down a US drone that it said was flying over Iran.
On Thursday, the Boxer transited through the Strait of Hormuz, a strategic waterway where one fifth of the world's oil passes.
The incidents follow the launch of the Trump administration's "maximum pressure" campaign of heightened sanctions that are aimed at forcing Tehran back to the negotiating table after the United States walked away from the Iran nuclear deal a year ago.