In a statement on Sunday, Hunt will meet European Union Foreign Ministers in Brussels on Monday to raise concerns about Iran breaching some of its commitments, reports the BBC.
The deal, which involves Iran limiting nuclear activities in return for the easing of economic sanctions, struggled after the US withdrew in 2018.
At the meeting, Hunt said he will work with the European partners of the deal - France and Germany - to encourage Iran to stick to its pledges.
"The Middle East is already one of the most unstable regions in the world, but if the different parties were armed with nuclear weapons it would represent an existential threat to mankind," he said in the statement.
In a joint statement issued ahead of the meeting, Britain, France and Germany on Sunday reiterated their support for the deal.
But said they were "deeply troubled" by recent events in the Gulf and "concerned" over US-Iran relations.
Earlier this month, the International Atomic Energy Agency confirmed that Iran had breached the deal's cap on stockpiling of low-enriched uranium, the BBC reported.
Iran said it was responding to sanctions reinstated by the US after Trump abandoned the deal last year. Last week it confirmed it will break another of the limits imposed by the deal.
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.
In response to the seizure, Iran threatened to seize a British oil tanker.
( With inputs from IANS )