Iran's Revolutionary Guards say the US navy fabricated evidence that a convoy of its ships was harassed by Iranian speedboats in Gulf waters on Sunday.
The US has released grainy footage, apparently showing small boats speeding near the American warships.
In an audio recording, an Iranian radio operator appears to say "I am coming at you; you will explode".
The Iranian parliamentary speaker has dismissed the affair as being part of a US propaganda campaign against Tehran.
"The footage released by the US Navy are file pictures and the audio has been fabricated," Iranian state-run TV quoted a Revolutionary Guards source as saying.
The US Pentagon says the American ships were about to open fire when the Iranian boats withdrew.
US President George W Bush described the incident as "provocative", adding that it was a "dangerous situation" that should not have happened.
The video, said to be shot from the bridge of the USS Hopper in the Strait of Hormuz, appears to show the small boats racing near the wake of the US ships and crossing close to each other.
One boat is shown in close-up - a blue speedboat with at least two crew.
After spotting the approaching vessels, a Navy crewman can be heard over the radio, warning them they are approaching a coalition warship.
"Request you establish communications, identify yourself and state your intentions, over," he says.
He refers to "five unidentified small surface" boats, and the ships' sirens can be heard in the background.
The four-minute video condenses what US officials have described as a 20-minute stand-off.
At the end of the US recording, the screen goes black and the remainder is in audio only. Some of the communication is unclear.
The US issues a final warning that if the boats do not change course immediately they will be "subject to defensive measures".
The speedboats, believed to belong to Iran's Revolutionary Guards, came within about 200m (650ft) of the US vessels, Pentagon officials said.
The weekend stand-off happened in a major oil shipping route, in what the Pentagon insists were international waters.
Iranian officials earlier played down the event, calling it an "ordinary occurrence".
An Iranian foreign ministry spokesman said: "This... happens for the two sides every once in a while and, after the identification of the two sides, the issue is resolved."