The latest hostilities followed Iran's announcement at the weekend that it was closing the vital waterway, casting further doubt on an interim deal to halt the war and driving oil prices higher.
"The Hormuz Strait is OPEN, and will remain OPEN, with or without Iran. We are reinstating THE IRANIAN BLOCKADE," Trump said on Truth Social on Monday, adding the US would collect a 20% toll on all cargo shipped through the strategic strait "as a matter of FAIRNESS".
He predicted more US strikes in an interview with conservative radio host Hugh Hewitt.
"We're going to hit them very hard tonight, and we're going to hit them hard tomorrow. And there's not a damn thing they can do about it," Trump said.
US Central Command began a third consecutive night of strikes against Iran shortly after the broadcast, at Trump's direction. Iran's semi-official YJC news agency said early on Tuesday that seven explosions were heard in the southern port city of Bandar Abbas and two more on Kish Island.
Iranian Foreign Minister Abbas Araqchi wrote on X that Tehran was the guardian of the strait and would remain so "forever", adding in response to Trump's comments that: "20 per cent is of course too much. We will be fair."
The United Nations' shipping agency pushed back against Trump's proposal, saying it opposes any fees for straits used in international navigation and stressing that there is no legal basis for introducing mandatory tolls on strait transits.
Trump has previously suggested the US could charge tolls on shipping through the strait, but has not done so and it remained unclear whether he would follow through this time.
The US Navy-led Joint Maritime Information Center said the blockade would take effect on Tuesday and apply to all vessel traffic regardless of flag, covering the entire Iranian coastline including ports and oil terminals.
It said the measure would not impede neutral transit passage through the strait to or from non-Iranian destinations, and that humanitarian shipments would be permitted subject to inspection.
Before the conflict began in February, around one-fifth of the world's oil and gas traffic passed through Hormuz daily, delivering more than 15 million barrels of fuel to global markets worth at least $US1.2 billion ($A1.7 billion). If the US were to impose a 20 per cent fee, it could generate around $US250 million ($A360 million) a day.
Iran has sought to establish a permanent fee and permit system of its own for vessels using the waterway.
Thousands of people have been killed in the war, mainly in Iran and Lebanon.
The latest exchanges mark an escalation over the past week, throwing into question the interim US-Iranian agreement signed last month to reopen the strait and halt hostilities.
The war, launched by the US and Israel, has destabilised the Gulf and spread across the region, with Iran attacking US bases in multiple countries.
US officials said around 20 vessels had been escorted through the strait in the previous 24 hours, although ship-tracking data showed little traffic moving. MarineTraffic said on Monday that vessel activity through the strait declined by about 52 per cent over July 10 to 12 compared to the previous week.
