Speaking at the White House on Thursday, Trump said that USS Boxer, an amphibious assault ship of the US Navy, destroyed the drone that threatened the US warship by flying within 1,000 yards of it and ignored multiple warning, Xinhua reported.
The semi-official Fars news agency reported that the Iranian Revolutionary Guard had seized the Stena Impero.
Iran's deputy foreign minister Abbas Aragchi tweeted: "We have not lost any drone in the Strait of Hormuz nor anywhere else". "I am anxious that USS Boxer has shot down their own [unmanned aircraft system] by mistake!"
"The drone was immediately destroyed".
On June 20, Iranian forces shot down a US surveillance drone over the Strait of Hormuz, claiming it had violated Iranian airspace, which the USA denied.
The move comes as tensions mount between the United States and Iran over the unravelling of the Obama-negotiated JPOA nuclear deal between Tehran and world powers.
The acknowledgement that a vessel has been seized by Iran's Revolutionary Guard appears to contradict statements by Iran's Foreign Ministry spokesman on Wednesday saying Iran had aided a foreign oil tanker with a malfunction.
At the time, Trump said he called off a retaliatory military attack on Iran at the last moment.
The company said the safety of their crew was paramount, and they had received no reports of injury to the ship's workers.
Less than a month earlier, Iran downed an American drone in the same waterway and Mr Trump came close to retaliating with a military strike.
Following the Gibralatar seizure earlier this month, British forces had been escorting ships that were flying the nation's flag, and it appeared oil tankers registered in the Isle of Man, Gibraltar and the United Kingdom had largely vacated the gulf.
The UK also has strained relations with Iran after Royal Marines seized a tanker carrying around $120m of oil off Gibraltar. US Central Command Spokesperson Bill Urban, in turn, stated that the unmanned aerial vehicle had been flying in global airspace over the Strait of Hormuz.
It claimed the ship - which was not named but is believed to be the Panamanian-flagged MT Riah - was smuggling a million litres of oil out of the country.
Tensions have escalated between the USA and Iran in recent weeks, after the Trump administration accused Tehran of planning to attack U.S. forces and interests in the region.
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