"The IRGCN boat was coming in at a high rate of speed. It did not respond to any signals, they did not respond to any bridge-to-bridge calls, they felt there was no choice except to fire the warning shots," the defence official told AFP on condition of anonymity.
The incident occurred at about 3am local time (0000 GMT) in the northern Persian Gulf, when the Iranian vessel began to approach the USS Thunderbolt.
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After the US ship fired the warning shots, the Iranian vessel stopped, the official said, at which point the Thunderbolt continued on her way.
The US Fifth Fleet, which is based in Bahrain and oversees the US ship involved, refused to immediately provide additional details.
The episode marks the latest in a series of close encounters between US ships and Iranian naval vessels.
In January, the USS Mahan destroyer fired warning shots at four Iranian Revolutionary Guard vessels that approached at high speed in the Strait of Hormuz.
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The Iranian Revolutionary Guards Corps is a paramilitary force that answers directly to the Islamic republic's supreme leader.
The force's boats periodically approach US warships in international waters and the Strait of Hormuz, ignoring US radio messages and giving little indication of their intentions.
In January 2016, the Iranians briefly captured the crew of two small US patrol boats that strayed into Iranian waters.
The 10 US sailors were released 24 hours later.
Tuesday's incident comes as the US Congress votes on a new sanctions bill against Russia.
The measure also includes sanctions against Iran and the IRGC navy - which stands accused of supporting terrorism - and North Korea, for its missile tests.
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