US Central Command said it began strikes on Monday at Trump's direction just after he told the Hugh Hewitt Show that Iran would be hit "very hard tonight, and we're going to hit them hard tomorrow. And there's not a damn thing they can do about it".
He later told reporters at the White House the US was attacking Iranian capabilities in the strait.
The UAE Ministry of Defence later said Iranian cruise missiles struck two Emirati oil tankers, the Mombasa and Al Bahiyah, while transiting the southern lane of the strait in Omani territorial waters, wounding one crew member and injuring eight others.
The United Kingdom Maritime Trade Operations agency said a tanker had been hit by an unknown projectile while travelling 40 nautical miles northeast of Oman's Qalhat and that all crew were safe.
The Islamic Revolutionary Guard Corps (IRGC) said two "offending" supertankers had been hit and disabled in the strait after ignoring repeated warnings and turning off navigation systems, Iranian media reported.
"The Hormuz Strait is OPEN, and will remain OPEN, with or without Iran. We are reinstating THE IRANIAN BLOCKADE," Trump had said earlier on Monday on Truth Social.
"The USA will be, from this point forward, known as 'THE GUARDIAN OF THE HORMUZ STRAIT', but as such, and as a matter of FAIRNESS, will be reimbursed, at the rate of 20% on all cargo shipped."
Iran's top joint military command said the US had no role in determining the future of the waterway and would not be allowed to intervene.
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: "Twenty per cent is of course too much. We will be fair."
Soon after the US military announced renewed strikes on Iran, Iranian media reported explosions in the port city of Bandar Abbas, Iran's Kish and Qeshm islands and on Abu Musa Island in the Gulf.
The incidents, which followed earlier exchanges of missile and drone attacks, extended the hostilities that 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.
Trump has previously suggested the US could charge tolls on shipping through the strait, but has not done so and it remains 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.
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 $US240 million ($A347 million) a day.
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. Thousands of people have been killed in the war, mainly in Iran and Lebanon.
MarineTraffic on Monday said vessel activity through the strait declined by about 52 per cent between July 10 to 12 compared to the previous week.
