Commander Bill Urban, the spokesman for the US Navy's Fifth Fleet, said the Iranian vessel came within 730 meters of the USS Bataan assault ship.
As a result, warning signals were sent to the vessel.
But in a statement issued via the IRGC's news site Sepah, it was the American "battleship" which moved towards one of Iran's patrol boats.
The incident happened at 3am local time today and involved the USS Thunderbolt, a Cyclone-class ship involved in an exercise with American and other vessels in the area.
The Navy characterized the Iranian boat's actions as not following internationally recognized "rules of the road ... creating a risk for collision".
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Unsafe interactions between US and Iranian vessels are far from uncommon. The Iranian craft was likely operated by the Iranian Revolutionary Guard Corps, which released a statement saying that a USA boat approached an Iranian patrol craft this morning.
The U.S. ship, the USS Thunderbolt, is a U.S. patrol ship. Those boats got as close as 890 yards. After the Iranian vessel did not respond to radio calls, flares, or warning sirens, US sailors were forced to fire warning shots.
The US slapped fresh economic sanctions on Iran earlier this month, designating 18 individuals and entities for supporting what it said were "illicit Iranian actors or transnational criminal activity".
Following that incident, a spokesman for the U.S. Navy's Fifth Fleet said, "Illuminating helicopters with lasers at night is unsafe, as it creates a navigational hazard that can impair vision and can be disorienting to pilots using night-vision goggles".
"Of note", he continued, "we actually had several other interactions with some smaller Iranian vessels following this one that were safe and professional".