The strikes come hours after US President Donald Trump dismissed an Iranian report of a deal to restore traffic through the strategic waterway.
The US official, who requested anonymity to speak candidly about military operations, told Reuters the military shot down four Iranian attack drones and struck a ground control station in the port city of Bandar Abbas that was about to launch a fifth drone.
A ceasefire between the US and Iran took effect in early April.
Iran's Tasnim news agency cited a military source as saying the Islamic Revolutionary Guards Navy fired toward a US oil tanker that was trying to transit the strait, forcing it to turn back.
The source said the US military then struck open ground around Bandar Abbas, with no casualties or damage reported.
Iranian media later reported that a military official said four vessels had tried to transit the strait early on Thursday, only to be turned back by warning shots fired in their direction.
The US military also carried out strikes in southern Iran on Monday, in what it described as defensive action but which Iran said was a "gross violation" of the ceasefire.
At a cabinet meeting attended by media, Trump dismissed an Iranian state TV report it had obtained an unofficial draft of an agreement to restore commercial shipping through the strait to prewar levels within a month, with Iran and Oman jointly managing traffic.
Trump said no single country would have control over the waterway, and appeared to threaten Oman, a country with which the United States has decades-long military and economic ties.
"Nobody's going to control (the strait)," Trump said.
"It's international waters and Oman will behave just like everybody else or we'll have to blow them up. They understand that, they'll be fine."
The US Treasury Department later added the Persian Gulf Strait Authority, the Iranian body set up to manage passage through the strait, to a list of sanctioned people and entities seen as posing threats to American national security.
Ebrahim Azizi, head of the Iranian parliament's national security committee, said Trump's "rhetoric" would not force Iran to back away from its demands to enrich uranium, wield authority over the strait and see sanctions against it lifted.
"It is obvious Trump, seeking a way out of this strategic deadlock, alternates between issuing threats and appealing for an agreement," Azizi said in a post on social media platform X.
Trump has also asked Saudi Arabia, Qatar, Pakistan, Turkey, Egypt and Jordan to join the Abraham Accords normalising relations with Israel as part of a deal to end the war, which they have declined to do.
Iranian state TV said the draft deal would also have the US withdraw military forces from the immediate vicinity, though it said the issue of American troops in the region needed further discussion.
The White House dismissed the report as a "complete fabrication". Tehran did not comment.
The Iranian TV report on the draft agreement did not mention Iran's nuclear program, which the US wants disbanded.
"The bottom line is Iran's never going to have a nuclear weapon," US Secretary of State Marco Rubio said at the cabinet meeting on Wednesday, US time.
Iran's Islamic Revolutionary Guards Navy said on Wednesday that 23 ships including oil tankers, container ships and other commercial vessels passed through Hormuz with its permission in the previous 24 hours, a fraction of the daily 125 to 140 vessels before the conflict.
With AP
