The Iranian Revolutionary Guard-affiliated news agency said the tanker was seized for breaking three regulations: shutting down its Global Positioning System; going through the exit of the Strait of Hormuz rather than the entrance; and ignoring warnings. In June, Trump said he called off a retaliatory strike on Iran following Tehran's move to shoot down an American drone.
Reuters says that Refinitiv data showed the Stena Impero is a British-flagged vessel owned by Stena Bulk.
According to CNN, the tanker is called Steno Impero and owned by Stena Bulk and managed by Northern Marine Management.
Iran's Islamic Revolutionary Guard Corps (IRGC), who published the footage, said it was taken "before and even after the time Americans claim" to have destroyed their drone.
The US has publicly blamed Iran for attacks on two oil tankers off the coast of Oman-which Iran has denied.
The U.S. was expected to take decisive military action against Iran, including the bombing of several military installations, but Trump reversed the order and said he was looking to deescalate the situation.
"Iran must cease this illicit activity and release the reportedly seized crew and vessel immediately".
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Reuters reported on Wednesday that shipping companies were hiring unarmed security guards for voyages through the Gulf. Iran said the vessel impounded was the same one it towed on Sunday after the ship had sent a distress call.
The British government said it was urgently seeking more information.
Around a third of the world's oil supplies travel through the Strait of Hormuz.
"I am extremely concerned by the seizure of two naval vessels by Iranian authorities in the Strait of Hormuz", British Foreign Secretary Jeremy Hunt said.
Last month, Iran downed an unmanned USA spy drone that it said violated Iranian airspace. "Last week, British warship blocked 3 Iranian vessels from seizing UK-flagged tanker".
The UK also has strained relations with Iran after Royal Marines seized a tanker carrying around $120m of oil off Gibraltar.
The claims from both sides mark another escalation of tensions between the two countries less than a month after Trump almost launched an airstrike.
Hossein Naghavi Hosseini, spokesman of the Iranian parliamentary committee on national security and foreign policy, said Trump's claim is part of an effort by the U.S.to "create tensions and psychological warfare in the region and in Iran, and hide its failures".