On Friday, the Stena Impero was seized by the Iranian Revolutionary Guard in the Strait of Hormuz after Tehran said it was “violating international maritime rules”.
A second tanker, the British-owned MV Mesdar, was also boarded by armed guards but released.
Video released by Iran’s Revolutionary Guard-affiliated Fars news agency appeared to show the moment the tanker was raided.
HMS Montrose was alerted but it was too far away to stop the seizure.
A recording of radio exchanges between a Royal Navy frigate and Iranian armed forces vessels moments before the tanker was seized was also released.
In the recording, an Iranian vessel tells HMS Montrose it wants to inspect the Stena Impero for security reasons.
Iran’s state-run IRNA news agency said the tanker was captured after it collided with a fishing boat and failed to respond to calls from the smaller craft.
But Mr Hunt said it was seized in Omani waters in “clear contravention of international law” and forced to sail into Bandar Abbas port in Iran.
The tanker’s owner, Stena Bulk, said it has made a formal request to visit the crew members.