The US Navy has destroyed an Iranian drone in the Strait of Hormuz after the aircraft threatened a ship, President Donald Trump says.

Trump told an event in the White House that the drone had flown to within 915 metre) of the USS Boxer.

"This is the latest of many provocative and hostile actions by Iran against vessels operating in international waters," Trump said on Thursday.

"The United States reserves the right to defend our personnel, facilities and interests.

"The drone was immediately destroyed." Trump gave no more details.

The Pentagon said in a statement that the USS Boxer, an amphibious assault ship, had taken "defensive action" against a drone, but did not mention if the aircraft was Iranian.

It said the incident happened at 10am local time on Thursday in international waters while the Boxer was transiting the waterway to enter the Persian Gulf.

"A fixed-wing unmanned aerial system approached Boxer and closed within a threatening range," chief Pentagon spokesman Jonathan Hoffman said in a written statement.

"The ship took defensive action against the UAS to ensure the safety of the ship and its crew."

Tensions in the Gulf region are high, with fears that the US and Iran could stumble into war.

The US has blamed Iran 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.

Earlier on Thursday, the US demanded Iran immediately release a vessel it seized in the Gulf.

A US military commander in the region said the United States would work "aggressively" to ensure free passage of vessels through the vital waterway.