Mohammed Ali Hosseini, an Iranian foreign ministry spokesman, earlier played down the incident, suggesting the Iranian boats had not recognised the US vessels.
According to US defence officials, five speedboats from the naval forces of Iran's Revolutionary Guards harassed three US warships on Sunday, as they sailed in the internationally recognised strait, three miles from Iranian waters.
US officials said the Iranian vessels dropped objects in the water ahead of the boats.
A defence department official quoted an Iranian radio transmission at the time as saying: "I'm coming at you and you will blow up in a couple of minutes."
'No special engagement'
But Iranian officials have expressed surprise at the US version of events, saying the encounter was a routine question of identification that ended with nothing special to report.
"What happened between the Guards and foreign vessels was an ordinary identification," Ali Reza Tangsiri, commander of the Guards naval forces in the region, told the Mehr news agency.
"No special engagement took place between the Guards and the foreign side," he said, adding that the Guards naval forces had a right to control and identify "any vessel entering Persian Gulf waters" to the northwest.
State television quoted an unnamed Guards source in the region as saying: "No threatening message was transmitted."
But Vice Admiral Kevin Cosgriff, commander of the US 5th Fleet based in Bahrain under whose command the allegedly harassed ships fall, told Al Jazeera he had a copy of the recording and that he was considering whether to release it.
Cosgriff also rejected the Iranians' claims that the incident was routine, saying it was "anything but ordinary" and that the Iranian ships had "manoeuvred aggressively".
Riad Kahwaji, from the Institute for Near East and Gulf Military Analysis, also told Al Jazeera: "I don't think it's routine to have five fast crafts encircle three big vessels ... from the US side."
Kahwaji questioned the motives of the Iranian Revolutionary Guards involved in the incident.
"Are we seeing here the so-called rogue elements of the Guards, who had kidnapped the British sailors, now at it again trying to provoke something with the Americans?" he said, referring to the seizure of 15 British sailors and marines in March last year.
"Could it be a political message at the time of Bush visiting the region?"
Alireza Ronaghi, Al Jazeera's correspondent in Tehran, said that although the Revolutionary Guard were not subject to the same disciplinary procedures as the navy, "at the same time they have a very tight command line and they are not allowed to provoke any other parties in the region".
There were no injuries in the incident, but US officials warned there could have been, as the Iranian boats turned away "literally at the very moment that US forces were preparing to open fire".
The US Fifth Fleet is based in Bahrain and US Navy officials say about three dozen US and allied warships are in the region at any one time.
Strait of Hormuz
The strait is 280km long and only 50km wide at its narrowest point.
It is of strategic importance as the only sea route through which oil from the various ports on the gulf can be transported. About 40 per cent of the world's traded oil supply passes through it.
Military action in the area would have a serious affect on oil exports, cutting off more than half of India's oil supply and almost all of that to Japan and South Korea.