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Iranian boats have tried to seize a British oil tanker in the Gulf before the fleet was warned off, US officials have said.

Three vessels, believed to belong to the Iranian Revolutionary Guard, approached the tanker while it was sailing through the Strait of Hormuz.

But British warship HMS Montrose, which reportedly had its 30mm deck guns trained on the boats, warned them off over radio.

It comes after Iranian President Hassan Rouhani said Britain would face "consequences" over the seizure of an Iranian tanker.

The UK's Royal Navy frigate had been escorting the British Heritage tanker from the rear as it was confronted by the boats on Wednesday.

"The Royal Navy HMS Montrose, which was also there, pointed it guns at the boats and warned them over radio, at which point they dispersed," one US official said.

"It was harassment and an attempt to interfere with the passage," another added.

A Ministry of Defence spokesman said three Iranian vessels had attempted to impede the passage of British Heritage. It was earlier reported there had been five boats.

"Contrary to international law, three Iranian vessels attempted to impede the passage of a commercial vessel, British Heritage, through the Strait of Hormuz," the spokesman said.

"HMS Montrose was forced to position herself between the Iranian vessels and British Heritage and issue verbal warnings to the Iranian vessels, which then turned away.

"We are concerned by this action and continue to urge the Iranian authorities to deescalate the situation in the region."

Defence officials had previously confirmed the Montrose was deployed to the region to perform a "maritime security role."

Iran's Revolutionary Guards rejected that they tried to stop the British tanker, the semi-official Fars news agency reported.

The incident occurred almost a week after British Royal Marines boarded an Iranian tanker, Grace 1, off Gibraltar and seized it on suspicion that it was breaking sanctions by taking oil to Syria.

Tensions between Iran, the US and its allies have risen sharply since Washington stepped up economic sanctions against Iran and moved to bring the country's oil exports to zero as part of a "maximum pressure" policy to make Iran halt actions that it said undermined regional security.

Iran has responded to the sanctions by starting to breach limits put on its nuclear activities under a 2015 deal with world powers.

Several oil tankers were attacked in waters near Iran's southern coast in May and June, for which the US blamed Iran. Tehran denied any involvement.

Last month, Iran shot down a US drone near the Strait of Hormuz, prompting President Donald Trump to order retaliatory air strikes, only to call them off.