He did not specify what Iran's next step would be, but Tehran warned last month it could reactivate centrifuge machines and ramp up enrichment of uranium to 20 per cent fissile purity.
The mission "will not be part of the United States maximum pressure policy on Iran because we remain committed to preserving the Iran nuclear agreement", Hunt said.
The sanctions have given rise to smuggling operations, industry analysts say, including efforts to mask the locations of large tankers transporting Iranian crude in defiance of USA sanctions.
"All sanctions should be lifted so that there will be no criminals facing us", he said, accusing the U.S. of committing acts of "economic terrorism" for blocking food and medicine imports.
Iran told European powers on Monday it would further reduce compliance with its 2015 nuclear deal in about a month's time if they were still failing to protect it from crippling USA sanctions, reimposed after Washington exited the deal.
The veteran diplomat also slammed Britain over its July 4 seizure of a tanker carrying Iranian oil. One-fifth of global oil consumption passes through the Strait from Middle East crude producers to major markets.
"A strait for a strait".
Iranian President Hassan Rouhani said on Tuesday that any war with his country would be "the mother of all wars", and insisted Iran be allowed free travel in the Strait of Gibraltar. "We remain committed to working with Iran and our worldwide partners to de-escalate the situation and maintain the nuclear deal".
It marks the Revolutionary Guard's third seizure of a vessel in recent weeks and the latest show of strength by the paramilitary force amidst an increase in regional tensions.
The move follows the seizure last month of the British-flagged tanker Stena Impero by Iranian Republican Guards in retaliation for the detention of an Iranian tanker off Gibraltar.
European nations have been reluctant to take part in the US naval mission, and Germany has said it will not be involved.
Tensions between Iran and the U.S. have been rising since Trump unilaterally withdrew the United States from the nuclear deal in May 2018 and began imposing sanctions as part of a "maximum pressure" campaign.
This new coordinated effort will bolster the work the United Kingdom has already being undertaking to this end, including through HMS Duncan and HMS Montrose accompanying UK-flagged ships.
Iran would argue that all of these incidents are responses, or deny that it had even carried out some of them.
Iraq's oil ministry said it had no connection to the vessel and that was working to establish what had happened.
"Iran will leave its 2015 nuclear deal with powers if necessary", Zarif said on Monday, adding that all measures taken by Iran were however "reversible if its interests under the deal are secured".
Tensions have soared since the Trump administration began stepping up a United States campaign of "maximum pressure" against Iran, with drones downed and tankers mysteriously attacked in Gulf waters.
Last month, the Iranian Revolutionary Guard said it had impounded the Panama-flagged MT Riah for alleged fuel smuggling as well as the British-flagged Stena Impero for breaking "international maritime rules".