An American official declined to comment on the claim.
The reported drone overflight comes after a series of naval incidents between Iran and the US in the greater Persian Gulf, including test rocket fire by the Islamic Republic and its brief capture of American sailors who strayed into its territorial waters.
The brief report by state television did not say what day the drone flight occurred, nor did it show any of the images of the aircraft carrier reportedly photographed by the drone. A story from the state-run IRNA news agency said an Iranian light submarine closely participated in the surveillance operation.
The Iranian report did not name the US vessel targeted. The nuclear-powered USS Harry S Truman, based out of Norfolk, Virginia, is in the Persian Gulf region launching airstrikes and supporting operations against the Islamic State group in Iraq and Syria.
Cmdr Kevin Stephens, a spokesman for the US Navy's 5th Fleet based in Bahrain, declined to comment on the Iranian report.
"I can say that we are confident in the ability of U.S. naval forces operating in the region to respond appropriately as the situation dictates, and will exercise our right to defend our forces against any threat," Stephens said.
Iran's navy began a naval drill this week over a 3- million-square-kilometer area including parts of the Strait of Hormuz, the Gulf of Oman and the Indian Ocean.
Iran said Wednesday its navy warned a US warship to leave an area of the naval drill. The US Navy later denied its operations were affected by the Iranian drill.
While Iran recently struck a nuclear deal with world powers including the US, its naval forces have continued its maneuvers. Iran has more than 2,000 kilometers of shoreline facing the Persian Gulf and the Sea of Oman.
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