The decision was disclosed as US President Donald Trump stepped up his war of words with the Islamic republic over its nuclear programme and its alleged support for terror groups in the Middle East.

"Iran better be careful," Trump told reporters outside the White House.

"They're treading on very dangerous territory. Iran, if you're listening, you better be careful."

British officials said the naval deployment was part of a pre-planned rotation and meant to ensure a continued British naval presence in one of the most important but volatile oil shipment routes in the world.

But a source said the switchover was brought forward by several days and should see two of Britain's most advanced warships jointly navigating the waters off Iran for a period that might last a number of weeks.

A government spokesman said the HMS Duncan was "deploying to the region to ensure we maintain a continuous maritime security presence while HMS Montrose comes off task for pre-planned maintenance and crew changeover".

Sky News television reported that HMS Duncan would not be part of the international military escort team for vessels in the Gulf proposed on Thursday by the United States.

HMS Duncan is an air defence destroyer that carries a set of heavy Harpoon anti-ship missiles and a crew in excess of 280.

The BBC reported that it had reached Turkey's Bosphorus Strait as it makes its way from the Black Sea through the Suez Canal to the Gulf.

HMS Montrose was forced to warn off three fast Iranian gunboats on Wednesday that UK officials said were trying to "impede" the progress of a British supertanker through the Strait of Hormuz in the Gulf.

Iranian officials have denied the incident ever happened.

- 'Very dangerous' -

The Strait of Hormuz episode occurred a week after UK Royal Marines helped the Gibraltar authorities detain an Iranian tanker that US officials believe was trying to deliver oil to Syria in violation of separate sets of EU and US sanctions.

Iran has bristled at the arrest and issued a series of increasingly ominous warnings to both the United States and Britain about its right to take unspecified actions in reprisal.

"If the enemy had made the smallest assessment they wouldn't have done this act," Iran's Revolutionary Guards deputy commander Ali Fadavi said on Thursday.

A source said the British government decided at the start of the week to raise the alert level for ships travelling through Iranian waters to three on a three-point scale.

The decision means that Britain views the security threat in Iranian waters for commercial ships as "critical".

But UK Foreign Secretary Jeremy Hunt called on Friday for "cool heads" to prevail as threats mount and Iran's response to its growing isolation -- and economic suffering from US sanctions -- becomes increasingly unpredictable.

"We want to do everything we can to make sure that we don't have an unintended escalation which could be very dangerous for the world," Hunt said.

- Gibraltar arrests -

The authorities of Gibraltar -- a British overseas territory on Spain's southern tip -- said on Friday that the Iranian supertanker was carrying 2.1 million barrels of light crude oil.

They also insisted that they had asked British Naval Marines to help with the Iranian tanker's arrest without any outside political pressure.

"These important decisions about breaches of our laws were certainly not decisions taken at the political behest or instruction of any other state or of any third party," Gibraltar's Chief Minister Fabian Picardo said.

The Gibraltar police on Thursday announced the arrest of the Iranian tanker's Indian captain and officer.

On Friday they detained two more Indian crew members as part of an "investigation of the suspected export of crude oil to the Banyas refinery in Syria".