Iran’s state television on Friday broadcast a video, provided by the country’s Revolutionary Guard, showing aerial views of ships which it said refuted the US assertion.
The television station said a drone captured the footage and that timing notations indicated the pilotless aircraft was still filming after Washington said it had been downed.
The video came shortly after US President Donald Trump said there was “no doubt” the US Navy had brought down an Iranian drone in the Strait of Hormuz on Thursday.
“No doubt about it, no. We shot it down,” Trump told reporters in the White House on Friday.
Trump said the US hopes “for their sake they don’t do anything foolish. If they do they will pay a price like nobody has ever paid a price.”
Earlier on Friday, a senior Trump administration official said Washington would destroy any drones that fly too close to its ships in the strategic Strait of Hormuz.
“If they fly too close to our ships, they’ll continue to be shot down,” the official told reporters at a briefing.
Tehran categorically denied US claims that a drone was brought down, saying all its craft were accounted for and jesting that American forces may have destroyed their own aircraft by mistake.
Al Jazeera’s Dorsa Jabbari, reporting from Tehran, said the Revolutionary Guard’s aerospace division described the footage as “hard evidence”.
“The footage appears to show this drone in the Strait of Hormuz … they monitored [the ship] for three hours,” she said.
“We can see that they managed to get pretty close to the warship, and they said that at no point was there any confrontation between the drone and the USS Boxer … What happened after their surveillance mission was complete was that this drone returned to its base and there was no incident,” Jabbari added.
According to her, Iranian authorities saw the accusation as a “repeat of a type of behaviour towards Iran carried out by the US government”.
“The Revolutionary Guards say the Americans are continuously trying to get the Iranians to react to their provocation,” she said.
On Thursday, Trump accused Iran of “hostile actions” against vessels operating in international waters, saying the US reserves the right to defend itself and that the drone was “immediately destroyed”.
In response, Abbas Araghchi, Iranian deputy foreign minister, dismissed the claim in a Twitter post.
“We have not lost any drone in the Strait of Hormuz nor anywhere else. I am worried that USS Boxer has shot down their own UAS [Unmanned Aerial System] by mistake!” he wrote on Friday.
Tensions in the Gulf are high, with fears that the US and Iran could stumble into outright military conflict.
Washington has blamed Tehran for a series of attacks since mid-May on shipping around the Strait of Hormuz, the world’s most important oil artery. Tehran rejects the allegations.
In June, Iran shot down a US military surveillance drone in the Gulf with a surface-to-air missile. Iran said the drone was in its airspace, but Washington said it was in international skies.
At the time, Trump said he called off a retaliatory military attack on Iran at the last moment.
Tensions between the two countries have escalated since last year when Trump withdrew the US from the 2015 Iran nuclear deal in which Tehran agreed to curb its nuclear programme in return for the lifting of sanctions.
Since then, the US has reinstated sanctions, saying it wants to renegotiate the accord and hold talks on Iran’s ballistic missiles programme and support for armed groups in the Middle East.