The official gave no other details, but it appeared the boat could have been mistaken as a threat in Gulf waters not far from Iran's maritime boundaries.
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Dozens of police and other Emirati officials crowded around the white-hulled boat, which sat docked after the incident in a small Dubai port used by fishermen and sailors.
The boat appeared to be a civilian vessel about 30 feet (9 meters) long and powered by three outboard motors. Similar boats are used for fishing in the region, though Iran's Revolutionary Guard also employs relatively small, fast-moving craft in the Gulf.
Rescue workers were seen carrying one person in a body bag off the boat and placing it in an ambulance as fishermen looked on. Officials moved the boat from the harbor shortly afterward.
Iranian naval drill (Archive photo: AP)
An Emirati rescue official at the scene confirmed the casualty toll. The officials spoke on condition of anonymity because of the sensitivity of the incident between the two allies.
US military vessels routinely cross paths with Iranian ships in international waters in the Gulf without incident, but speed boats from Iran's Revolutionary Guard have passed close to US ships in incidents that have raised alarm in Washington.
In early 2008, then President Bush accused Iran of a "provocative act" after five small Iranian craft buzzed around the destroyer USS Hopper.
Tensions are elevated in the Gulf after Iran last week renewed threats to close the strategic Strait of Hormuz - the route for one-fifth of the world's oil - in retaliation for tighter sanctions over Tehran's nuclear program. The US recently boosted its naval presence in the Gulf with additional minesweepers and other warships.
The US Navy's 5th Fleet, based in Bahrain, said it was investigating the Monday shooting. The US Embassy in Abu Dhabi had no immediate comment, referring all questions to the Navy.
Emirati officials could not be reached for comment.