The USS Abraham Lincoln made its second voyage through the strategic waterway in two weeks.
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Iranian patrol boats followed the ship and at one point came "within about half a mile" of the Lincoln, according to a BBC journalist on board. Radar operators also picked up an Iranian drone and surveillance helicopter in Iran's airspace near the strait, the Associated Press said.
The Lincoln was accompanied by a US cruiser and a destroyer, as well as several US helicopters.
On its previous voyage last month, it was protected by French and British naval vessels, a move seen as a demonstration of international support for keeping Hormuz open.
The carrier passed through the strait "without incident" on Jan. 23, despite threats from Iran of unspecified action if US ships entered the waterway.
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Earlier this week, the US Navy warned that Iran had built up its naval forces in the Gulf, including submarines, fast-attack craft and boats fitted with large warheads, Reuters reported.
American forces are ready and able to prevent it blocking the Strait of Hormuz, however, according to Vice Admiral Mark Fox, the head of the Fifth Fleet.
Iran has threatened to close the waterway in response to international sanctions on its oil exports.
Iran has adopted a strategy of "smart control of the Strait of Hormuz," the commander of the Iranian Revolutionary Guards said this week. According to Major General Mohammad Ali Jafari, cited by the Tehran Times, Iran now has the upper hand: "We have entered a new phase," he said, "and now these are our threats that affect the enemy."