The encounter happened when the Nimitz-class nuclear-powered supercarrier USS John C. Stennis and its strike group were returning to the Persian Gulf, breaking the longest US carrier absence in the region since at least 9/11.
Some 30 IRGC vessels reportedly followed the carrier and its accompanying warships, at one point launching rockets nearby, Associated Press reported.
A commercial-grade drone was also said to have flown by, and one Iranian ship could be seen with photographers and journalists observing the aircraft carrier, the report said.
There was no immediate reaction to the report by Iranian authorities.
The encounter came right before the start of massive war games across Iran’s south on Saturday.
The military exercise is held on Qeshm Island, located off the coast of Iran’s Hormozgan province and near the Strait of Hormuz, where about one-third of the global oil shipments passes through.
Tensions between Iran and the US have escalated since early 2017, when Donald Trump came to power in the US to harden Washington’s line on Iran.