The timing of the exercise is unusual, as it appears to be similar in scale and nature to a drill that ordinarily happens later in the autumn.
The official, speaking on condition of anonymity, said several dozen boats were out training early Thursday morning.
The vessels are mostly small attack boats, and there have been no interactions with US ships in the area, the official added.
Trump, Iran and talks
In a statement, Captain Bill Urban, the military's Central Command spokesperson, said the US was "aware of an increase" in Iranian naval operations in the Gulf, the Strait of Hormuz and the Gulf of Oman.
"We are monitoring it closely, and will continue to work with our partners to ensure freedom of navigation and free flow of commerce in international waterways," Urban said.
The exercises come at a time of increased tension between Iran and the United States, which has pulled out of a historic nuclear pact and is slapping fresh sanctions on Tehran on Monday.
US officials in recent years have accused both the regular Iranian navy and the Iranian Revolutionary Guards Corps of routinely harassing American warships in the Gulf.
Trump predicts Iran talks 'pretty soon'
But so far this year, to the befuddlement of some military officials, there have been no such incidents.
The Iranian Revolutionary Guards Corps is a paramilitary force that answers directly to the Islamic republic's supreme leader.
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.
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