The foreign secretary rallied for the action as he condemned the detention of the Stena Impero by Iranian Revolutionary Guards on Friday as an "act of state piracy".
Following a meeting of the Government's Cobra emergencies committee, Tory leadership hopeful Mr Hunt said "constructive discussions" had taken place with a number of countries over the preceding 48 hours.
The proposed new European mission would focus on ensuring free navigation through one of the world's most important waterways, which carries a fifth of the world's oil and a quarter of its liquefied natural gas flow, he said.
It would seek to "complement" US proposals to protect shipping in the region, he said in a statement to the Commons.
However, it would not form part of the American "maximum pressure" policy on Tehran as the UK continued to support the Iran nuclear which the US has repudiated.
"It is with a heavy heart that we are announcing this increased international presence in the Gulf, because the focus of our diplomacy has been on de-escalating tensions in the hope that such changes would not be necessary," Mr Hunt said.
"If Iran continues on this dangerous path, they must accept the price will be a larger Western military presence in the waters along their coastline, not because we wish to increase tensions but simply because freedom of navigation is a principle which Britain and its allies will always defend."
He said British-flagged shipping was being advised against travelling in Iranian waters and the entire Strait of Hormuz.
Mr Hunt also said said the Royal Navy "has become too small" and extra funding must be found by the next prime minister - which could be him should he cause an upset and defeat frontrunner Boris Johnson.
Conservative MP John Baron asked if Mr Hunt agreed that a Royal Navy of fewer than 20 ships is "not up to the task" and called for increased defence spending.
Mr Hunt replied: "I might be straying slightly from my brief as Foreign Secretary but it won't surprise (Mr Baron) to know I am a supporter of increased spending on our armed forces.
"We had in many ways a golden period after the fall of the Berlin Wall where there was a peace dividend and we were able to reduce defence spending, but now we have to recognise there are increased dangers in the world - both in the Middle East and because Russia has become much more aggressive than it was previously.
"I think the navy in particular has become too small so I hope whoever the next prime minister is will reflect carefully on what we can do to bolster our great Royal Navy."
Prior to Mr Hunt's statement, Theresa May, senior ministers and security chiefs met to discuss the UK's response to the Gulf crisis following the seizure of a British-flagged tanker by Iran.
Downing Street has been hit by claims that the Government "dropped the ball" by failing to prepare for Tehran's actions against British shipping in the Strait of Hormuz.
The Prime Minister chaired a meeting of the Government's emergency committee Cobra and officials said the meeting would consider the options for "strengthening current reassurances" to commercial shipping, as well as the response to Tehran.
The Prime Minister's official spokesman said: "We do not seek confrontation with Iran but it is unacceptable and highly escalatory to seize a ship going about legitimate business through internationally recognised shipping lanes."