USS Dwight D. Eisenhower seen in November 2016, (Navy)
The unverified footage shows jets on the 41-year-old Nimitz-class ship's deck and may raise questions about how a drone could get so close to an aircraft carrier, which has been called the "signature expression of American power."
The report included footage that claimed to be produced by the Guard. It was unclear when the footage was taken. A U.S. Naval Forces Central Command spokeswoman told CBS News that that particular aircraft carrier has not been in the Persian Gulf since 2016. She said the U.S. and its allies are committed to freedom of navigation in the Strait of Hormuz.
The strait, which sees nearly a third of all oil traded by sea pass through it, has been the scene of past confrontations between the U.S. and Iran, including a one-day naval battle in 1988. In recent years, the U.S. Navy has accused Iranian patrol boats of harassing American warships in the waterway.
The drone that took the footage is an Ababil-3 with an eight-hour flight capability at 12,000 feet and a 155-mile range.
The Trump administration said Monday that it will no longer exempt any countries from U.S. sanctions if they continue to buy Iranian oil, stepping up pressure on Iran in a move that primarily affects the five remaining major importers: China and India and U.S. treaty allies Japan, South Korea and Turkey. The move is part of the administration's "maximum pressure" campaign on Iran that aims to eliminate all of its revenue from oil exports, which the U.S. says are used to destabilize the region.
Iran reiterated its long-running threat to close the Strait of Hormuz if it's prevented from using the crucial waterway in the Persian Gulf, through which about a third of all oil traded at sea passes.
In 2016, Iran's navy similarly took video footage of the nuclear-powered carrier USS Harry Truman, based in Norfolk, Virginia, while it was in the Persian Gulf region launching airstrikes and supporting operations against the Islamic State group in Iraq and Syria.
Fox News' Edmund DeMarche and The Associated Press contributed