Trump's early morning post on social media came shortly after the US military seized another tanker associated with the smuggling of Iranian oil, ratcheting up a stand-off over the strait through which 20 per cent of all crude oil and natural gas traded passes.
"I have ordered the United States Navy to shoot and kill any boat, small boats though they may be ... that is putting mines in the waters of the Strait of Hormuz," Trump posted.
"There is to be no hesitation. Additionally, our mine 'sweepers' are clearing the Strait right now."
"I am hereby ordering that activity to continue, but at a tripled up level!" Trump added.
He also said the military is intensifying mine clearing operations in the critical waterway.
His post did not mention steps to deal with the other means Iran has used to block shipping along the route: mainly speedboats, missiles and drones.
The move comes a day after Iran's paramilitary Revolutionary Guards attacked three cargo ships in the strait, capturing two of them.
State television broadcast footage overnight of masked troops pulling up in a grey speedboat alongside the MSC Francesca, climbing a rope ladder to a shell door in the hull and jumping through brandishing rifles.
The footage, presented with an action-movie-style soundtrack and no commentary, also included views of another ship, the Epaminondas.
Iran said it had captured both on Wednesday, accusing them of trying to cross the strait without permits.
Iran's judiciary chief Gholamhossein Mohseni-Ejei said the merchant vessels attacked in the strait had "faced the law".
Iranian speedboats and marine drones were sheltering in sea caves off an island near the strait and keeping the US navy from approaching, he said.
The US Defense Department released video footage earlier on Thursday of US forces on the deck of the Guinea-flagged oil tanker Majestic X, which was seized in the Indian Ocean.
"We will continue global maritime enforcement to disrupt illicit networks and interdict vessels providing material support to Iran, wherever they operate," a Pentagon statement said.
Ship-tracking data showed the Majestic X in the Indian Ocean between Sri Lanka and Indonesia, roughly the same location as the oil tanker Tifani, earlier seized by US forces.
It had been bound for Zhoushan, China.
The vessel previously had been named Phonix and had been sanctioned by the US Treasury Department in 2024 for smuggling Iranian crude oil in contravention of US sanctions on the Islamic Republic.
On Tuesday, Trump extended a ceasefire while maintaining a US blockade of Iranian ports.
There was no immediate sign whether peace talks, previously hosted by Pakistan, would resume anytime soon.
The stand-off between the US and Iran has effectively choked off nearly all exports through the strait with no end in sight.
Since the February 28 start of the war between Iran, Israel and the United States, more than 30 ships have come under attack in the waters of the Persian Gulf, the Strait of Hormuz and the Gulf of Oman.
with Reuters
10°C