The Stena Impero is British-flagged and the Mesdar is Liberian-flagged but British owned.
The Stena Impero's owners say they have been unable to contact their vessel, which was "heading north towards Iran".
They say there are 23 personnel on board the British-flagged oil tanker and it was approached by "unidentified small crafts and a helicopter".
Tracking websites suggest the Mesdar may be back on course and was stopped only briefly.
The government's emergency committee, Cobra, is meeting in Whitehall later for the second time on Friday to discuss the incident.
Mr Hunt said the seizures were "unacceptable" and the emergency meeting would review what the UK could do to "swiftly secure the release of the two vessels".
"It is essential that freedom of navigation is maintained and that all ships can move safely and freely in the region," he added.
He said the tankers' crews were made up of a range of nationalities but no British citizens were understood to be on board either vessel.
"Our ambassador in Tehran is in contact with the Iranian Ministry of Foreign Affairs to resolve the situation and we are working closely with international partners," he said.
These latest developments come amid heightened tensions between the UK, the US, and Iran.
Saturday 20 July 2019 02:05