Planes were already in the air and ships in position when the order came to stand-down, according to reports.
The US was planning to launch an attack against Iran on Thursday night but called it off at the last minute, according to a report.
An unnamed US official told the Associated Press that US President Donald Trump had approved military strikes on targets such as radar and missile batteries but had pulled back.
The New York Times reported planes were already in the air and ships in position when the order came to stand-down, according to unnamed administration officials. No missiles were fired.
Iranian state TV shows what it says are sections of the downed drone
The US says its surveillance shows the drone was shot down over the Strait of Hormuz
It was not clear whether Mr Trump changed his mind or whether there was a more strategic reason.
It was also unclear whether the attacks would go ahead at a later date.
Mr Trump had been asked earlier in the day what his response to Iran might be and he said: "You'll soon find out."
The words came after he had spent most of the day discussing Iran with national security advisers, having earlier said that Iran had made a "very big mistake".
Iranian state television on Friday showed what it said were retrieved sections of a US military drone shot down on Thursday.
Amirali Hajizadeh, head of the Revolutionary Guards aerospace division, told a reporter the wreckage was proof the drone had been over Iranian territorial waters when it was shot down by his forces.
The US Federal Aviation Administration on Thursday issued an emergency order banning US operators from flying over part of airspace over the Strait of Hormuz and Gulf of Oman.
The US military has denied it had a drone over Iran. File pic
It said that the nearest civil aircraft had been around 45 nautical miles from the Global Hawk drone when it was shot down and it was concerned about escalating tensions in the area.
It added: "There were numerous civil aviation aircraft operating in the area at the time of the intercept."
Iran's military released a video it claims shows a US surveillance drone being shot down
A United spokesman said customers flying from Mumbai to Newark would be booked on alternative flights back to the US, while American Airlines and Delta Air Lines said they do not fly over Iran.
The FAA's order does not affect non-US carriers - but British Airways said on Friday that it was re-routing flights away from the Strait of Hormuz.
It joins Australia's Qantas, Dutch carrier KLM and German airline Lufthansa.
BA said: "Our safety and security team are constantly liaising with authorities around the world as part of their comprehensive risk assessment into every route we operate."
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