Hunt said parliament would be updated on Monday about what further measures the British government would take.
In an undated image made from video provided by Stena Bulk, the British oil tanker Stena Imperio at sea.
"Our priority continues to be to find a way to de-escalate the situation", he said.
Hunt said the COBR meeting was called to review what in known and what can be done to swiftly secure the release of the two vessels - a British-flagged vessel and a Liberian-flagged vessel.
Defence Secretary Penny Mordaunt described the incident as a "hostile act" and told Sky News the frigate was 60 minutes away from being able to help.More news: New boss of BMW 'will provide brand with fresh momentum'
The Philippines also said it would ask Iran to free a Filipino crew member on the Swedish-owned Stena Impero which was seized on Friday, as tensions mount in a key waterway for the world's oil supplies.
Prime Minister Theresa May of Britain convened an emergency meeting of advisers late Friday to respond.
"If freedom of navigation is restricted Iran is the biggest loser, it is in their interests to resolve this situation as quickly as possible".
"This is completely unacceptable", Hunt said.
"Trump tearing up the Iran nuclear deal has fuelled confrontation".More news: Taliban twin attack kills 9, injures 30 in Pakistan's Dera Ismail Khan
"This is about the safety and security of British and global shipping in one of the most important seaways in the world, and that is why we're calling on Iran to reverse this illegal act", he said. And so, we spent a long time this afternoon in COBR discussing how we can guarantee the security of British and global shipping.
Tensions between Britain and Iran spiked earlier this month when the British military impounded an Iranian tanker near Gibraltar on suspicion of having violated a European Union embargo on the sale of oil to Syria.
The audio released Sunday by Dryad Global shows how the Royal Navy was unable to prevent the ship's seizure by Iranian forces.
But Iran's supreme leader Ayatollah Ali Khamenei called the tanker's seizure an act of "piracy" on Tuesday and warned the United Kingdom to expect a response.More news: Progress in US-China talks stall, Huawei remains on the table