The Stena Impero is British-flagged and the Mesdar is Liberian-flagged but British owned.
The Mesdar's operator said the vessel was now free to continue its journey after it was boarded by armed guards at around 17:30 BST on Friday.
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".
The Mesdar's Glasgow-based Norbulk Shipping UK said communication had been re-established with the vessel and its crew was "safe and well".
The government's emergency committee, Cobra, is meeting in Whitehall 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.
Iranian media reported Stena Impero had been seized by the Iranian Revolutionary Guard.
The Tasnim news agency quoted the Ports and Maritime Organisation of Iran as saying: "We received some reports on the British oil tanker, Stena Impero, causing problems.
"We asked the military forces to guide this tanker towards Bandar Abbas port to have the required investigations carried out."
Stena Bulk, the vessel owner, and Clydebank-based ship manager Northern Marine Management confirmed the UK-registered Stena Impero was approached at around 16:00 BST on Friday while it was in international waters.
A statement said there were no reported injuries and the safety of the crew was the priority of the tanker's owners and managers.
Tensions between the UK and Iran flared up earlier this month when Royal Marines seized an Iranian tanker which was suspected of breaking EU sanctions.
The UK suspected Grace 1, detained on 4 July near Gibraltar, was carrying oil bound for Syria.
In response to the seizure, Iran threatened to seize a British oil tanker.
On 9 July, the UK raised the threat to British shipping in Iranian waters in the Gulf to "critical" - the highest level.
A day later, Iranian boats attempted to impede a British oil tanker in the region, before being warned off by a Royal Navy ship, according to the Ministry of Defence.
Iran denied any attempted seizure.
Labour deputy leader Tom Watson tweeted that the latest reports were of "real concern", adding that "any move to seize a British tanker would be a significant and harmful escalation of a situation where de-escalation is needed".
Sir Richard Dalton, former UK ambassador to Iran, told the BBC that Iran was "trying to put a scare into the owners and operators of tankers" in the region.
The Mesdar's operator said the vessel was now free to continue its journey after it was boarded by armed guards at around 17:30 BST on Friday.
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".
The Mesdar's Glasgow-based Norbulk Shipping UK said communication had been re-established with the vessel and its crew was "safe and well".
The government's emergency committee, Cobra, is meeting in Whitehall 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.
Iranian media reported Stena Impero had been seized by the Iranian Revolutionary Guard.
The Tasnim news agency quoted the Ports and Maritime Organisation of Iran as saying: "We received some reports on the British oil tanker, Stena Impero, causing problems.
"We asked the military forces to guide this tanker towards Bandar Abbas port to have the required investigations carried out."
Stena Bulk, the vessel owner, and Clydebank-based ship manager Northern Marine Management confirmed the UK-registered Stena Impero was approached at around 16:00 BST on Friday while it was in international waters.
A statement said there were no reported injuries and the safety of the crew was the priority of the tanker's owners and managers.
Tensions between the UK and Iran flared up earlier this month when Royal Marines seized an Iranian tanker which was suspected of breaking EU sanctions.
The UK suspected Grace 1, detained on 4 July near Gibraltar, was carrying oil bound for Syria.
In response to the seizure, Iran threatened to seize a British oil tanker.
On 9 July, the UK raised the threat to British shipping in Iranian waters in the Gulf to "critical" - the highest level.
A day later, Iranian boats attempted to impede a British oil tanker in the region, before being warned off by a Royal Navy ship, according to the Ministry of Defence.
Iran denied any attempted seizure.
Labour deputy leader Tom Watson tweeted that the latest reports were of "real concern", adding that "any move to seize a British tanker would be a significant and harmful escalation of a situation where de-escalation is needed".
Sir Richard Dalton, former UK ambassador to Iran, told the BBC that Iran was "trying to put a scare into the owners and operators of tankers" in the region.
