The Pentagon insists the US vessels were in international waters
US Secretary of State Condoleezza Rice has described the actions of Iranian vessels which confronted the US Navy as provocative and dangerous.
Iran played down the event, calling it an "ordinary occurrence", but Ms Rice told the BBC there was "nothing normal" about the incident.
The US says five Iranian speedboats challenged three US ships in the Strait of Hormuz, threatening to blow them up.
It says the Iranians withdrew as the US ships prepared to open fire.
Ms Rice told the BBC Arabic service: "It was provocative, and that kind of provocation is dangerous.
"I would sincerely hope that the Iranians would refrain from any such activity."
And she warned that the United States was committed to staying in the Gulf.
"The United States under this president has sent a very strong signal that America has strong interests in the Gulf, that the United States will continue to defend its interests in the Gulf, and this goes back for decades," she said.
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."
'You will explode'
The incident happened in a major oil shipping route.
The speedboats, believed to belong to Iran's Revolutionary Guards, came within about 200m (650ft) of the US vessels, Pentagon officials said.
"I am coming at you. You will explode in a couple of minutes," the Iranians said in a radio transmission, according to US officials.
Five Iranian speedboats "swarm" US ships at about 0400 GMT
US ships receive radio call threatening to blow them up
US ships radio Iranian speedboats and sound ships' whistles
Speedboats approach within 200 metres of US ships
US ships ready their guns
Speedboats depart, no shots fired
Source: Pentagon and US Navy officials
The US said their ships were about to open fire when the Iranian boats withdrew.
The confrontation, which occurred at about 0400 local time on Sunday or late on Saturday in Washington, lasted about 20 minutes, according to the US.
The Pentagon has insisted that the three US vessels - identified as navy cruiser USS Port Royal, destroyer USS Hopper and frigate USS Ingraham - were in international waters.