The US military has conducted strikes on Iranian targets after President Donald Trump accused Iran of a "foolish violation" of its truce following an attack on a cargo ship in the Strait of Hormuz.

No casualties were reported when the ship was struck by a one-way attack drone on Thursday, an incident which prompted a planned evacuation of more than 11,000 sailors stuck in the region.

In response, US Central Command said on Friday it had struck missile and drone storage facilities and coastal radar positions. There has been no comment yet from Iran.

Just moments before the strikes were announced, President Trump said "you'll see" when asked if the US would respond to the Iranian attack.

US Central Command - or Centcom - described the strikes as "a powerful response" to the drone attack in a statement.

"The unwarranted aggression against commercial shipping by Iranian forces clearly violated the ceasefire," it also said.

"Furthermore, Iran's dangerous behavior undermined freedom of navigation as commerce increasingly flows through the vital international trade corridor."

Centcom said the US military would "continue to provide safe passage coordination and support to commercial vessels transiting the strait".

After US and Israeli attacks against Iran began at the end of February, Tehran effectively closed the strait - a critical waterway for oil and gas shipments - causing a spike in global oil prices and choking off shipments of other crucial commodities such as fertiliser.

The US and Iran agreed on 17 June to end hostilities under a 14-point memorandum of understanding, which had also called for Iran to use its "best efforts for the safe passage of commercial vessels with no charge for 60 days".

Speaking to reporters at the White House on Friday afternoon, Trump refused to be drawn into questions on how the US might respond, or whether he viewed the ceasefire as still intact.

"You'll find out," he said. "I don't like the fact that they took a shot yesterday. They shouldn't be doing that."

Asked why he believed Iran would conduct such an operation, Trump said only that "they're a little bit different".