A U.S. official said any disruption of traffic will not be tolerated. The acting commander of Iran's revolutionary guard rejected the warning.
Iran threatened to close the strait if Washington imposes sanctions targeting Iran's crude exports.
Meantime, the official IRNA news agency reported on Thursday that an Iranian surveillance plane recorded video and photographed a U.S. aircraft carrier as it was entering the Gulf of Oman from the Persian Gulf during Iran's ongoing navy drill.
The report did not provide details and it was unclear what information the Iranian military could glean from such footage.
The news agency quoted Iran's navy chief as saying that it shows Iran has "control over the moves by foreign forces" in the area.
A spokeswoman for the U.S. 5th Fleet said the aircraft carrier USS John C. Stennis and guided-missile cruiser USS Mobile Bay headed out from the Gulf and through the Strait of Hormuz on Tuesday, after a visit to Dubai's Jebel Ali port. She said the passage through the strait was routine and preplanned.
The Associated Press contributed to this story.