Britain has raised the security alert for British-flagged ships in the Gulf to its highest level, Sky News understands.
The Department for Transport lifted the security code for commercial tankers and other vessels to level three - critical - in the early hours of Tuesday.
It means ships are advised to avoid Iranian territorial waters if possible or minimise their exposure while passing through the Strait of Hormuz and elsewhere along the coast.
British-flagged ships have been advised to keep alert for Iranian patrol boats "being aggressive towards them", a maritime source said.
The US Navy's Fifth Fleet says it will work closely with the Royal Navy and other partners to defend the freedom of navigation.
Vice Admiral Jim Malloy, Commander US Fifth Fleet added: "The United States Fifth Fleet is aware of the Islamic Revolutionary Guard Corps Navy's unlawful harassment and attempts to interfere with the passage of the UK-flagged merchant vessel British Heritage on 10 July, near the Strait of Hormuz."
It comes after three Iranian boats tried to stop a British oil tanker in the Strait of Hormuz off Iran's coast.
HMS Montrose, a British warship operating in the area, then gave a warning and deployed its helicopter, a wildcat, which circled the Iranians, before their boats withdrew.
A government spokesman said: "We are concerned by this action and continue to urge the Iranian authorities to de-escalate the situation in the region."
An unnamed US official told AP their aircraft was in the region at the time the boats attempted to block the tanker and the US has video footage.
Tensions have been high since an Iranian supertanker - the Grace 1 - was boarded by Royal Marines amid suspicion it was taking crude oil to Syria, in breach of EU sanctions.
Today police in Gibraltar arrested the captain and the chief officer of the vessel. They have been interviewed but not charged and the investigation is ongoing.
A shipping industry source said his vessels are increasing the number of watch keepers on deck while close to Iran, trying to move through the strait during daylight hours and travelling at a faster pace than usual to keep safe.
A Department for Transport spokeswoman said: "The Department for Transport, as competent authority, regularly provides Security Advice to UK and Red Ensign Group Shipping on how they should operate in areas of high risk."
Some 15 to 30 British-flagged tankers and other large ships are in the Persian Gulf on a daily basis. At least one to three pass through the Strait of Hormuz every 24 hours.
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US President Donald Trump tweeted on Thursday afternoon, quoting a talk show host who said: "It seems that the Brits and the French and the Germans are coming around to the idea that the Iranians are up to no good."
The dispute is part of a wider struggle over the Iran nuclear deal that Donald Trump has ditched but Europe wants to save, writes Deborah Haynes
Tory leadership contender Boris Johnson said the UK should continue to be "very, very tough on Iran", saying there is "value" in the Iran Nuclear deal. He added: "Iran is a very destabilising force, so I think we should be trying to constrain Iran politically and diplomatically."
His rival for number 10, Jeremy Hunt, said the latest row "shows exactly why we must invest more in defence. We have run down our Navy too much and this must now be urgently reversed."
Iran's Revolutionary Guard has denied claims of a confrontation, saying: "There were no clashes with alien boats, especially English boats."
Iranian President Hassan Rouhani warned the UK of "consequences" after the seizing of the Grace 1.
"You [Britain] are the initiator of insecurity and you will realise the consequences later," Rouhani said after a cabinet meeting on Wednesday, according to the semi-official news agency Tasnim.
The US has been leading a push for allies and other tankers that use the Strait of Hormuz to increase their maritime security in the region, safeguarding strategic waters off Iran and Yemen.
It alleges that Tehran was behind attacks on six oil tankers in the area.
Relations between the two countries have fractured since Mr Trump pulled the US out of a nuclear deal with Iran and re-imposed sanctions.