The UK is to increase its military presence in the Gulf by sending a second warship to the region.
Tensions are mounting in the Gulf after a Royal Navy warship deterred Iranian patrol boats attempting to impede a British tanker sailing through the Strait of Hormuz.
Iran has also demanded the immediate release of its oil tanker captured off the coast of Gibraltar, warning the UK: "This is a dangerous game and has consequences."
The Grace 1 tanker was seized last week after it was suspected of taking crude oil to Syria in breach of EU sanctions.
HMS Duncan, a Type 45 Destroyer, will sail to the Gulf in the coming days after recently completing NATO exercises in the Black Sea.
Duncan will operate alongside the Royal Navy frigate HMS Montrose, and US allies in the Gulf, but she will not be part of an international maritime coalition proposed by Washington.
It is understood that Duncan was always due to travel to the region to give some relief to HMS Montrose.
However, her deployment has been brought forward as a result of the deepening crisis with Iran.
In addition to HMS Montrose, the UK also has four mine hunters permanently stationed in the region, and a Royal Fleet Auxiliary ship.
Prime Minister Theresa May's official spokesman said discussions were ongoing between UK and US about increasing their military presence in the Gulf.
Foreign Secretary Jeremy Hunt said it was "time for cool heads", adding: "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."
However a senior Iranian cleric, Kazem Sedighi, warned Britain will soon be "slapped in the face" for "daring" to capture the Iranian supertanker Grace 1.
Police in Gibraltar arrested two officers from the Grace 1 on Friday, having previously detained the captain of the vessel's captain and chief officer.
The four men, who are Indian nationals, have been arrested over alleged breaches of EU economic sanctions against Syria, but none have been charged as yet.
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Calling for the release of its oil tanker, a spokesman for Iran's foreign ministry told the state news agency IRNA: "This is a dangerous game and has consequences.
"The legal pretexts for the capture are not valid... the release of the tanker is in all countries' interest."
Iran's foreign minister Mohammad Javad Zarif accused the UK of being "servants of America" and said the EU sanctions in question were intended to stop Europe buying Syria's oil, not countries on other continents.
"This is a very childish and ridiculous excuse by the British," he said.
"They should officially announce that we are servants of America and act on behalf of America. America has returned their favour well by insulting their ambassador and their prime minister."
Mohammed Marandi, a professor at Tehran University, also claimed the seized Iranian tanker was too big for Syrian ports so could not have been carrying cargo to the war-torn country.
He told Sky News: "The whole notion that Europeans have the right to strangle nations to get their way is something that people in this part of the world view very differently than in Europe.
"Iranians see this as an act carried out at the behest of the United States."
However, Gibraltar has insisted its decision to detain the Iranian tanker was taken alone and not on the orders of the UK government.
The territory's chief minister said Fabian Picardo said: "There has been no political request at any time from any government that Gibraltar should act or not act on one basis or another."
The vessel contained 2.1 million barrels of light crude oil, he added.
The UK government said on Thursday that three Iranian vessels tried to block a British-owned tanker passing through the Strait of Hormuz, which controls the flow of Middle East oil to the world, but backed off when confronted by HMS Montrose.
Iran's Revolutionary Guard denied claims of a confrontation, saying if it had received orders to seize any ships it would have executed them immediately.
Sky News understands British ships have been warned to keep alert for Iranian patrol boats "being aggressive towards them".
Some 15 to 30 British-flagged tankers and other large ships are in the Persian Gulf on a daily basis. Between one and three pass through the Strait of Hormuz every 24 hours.
The UK government said HMS Duncan is going to the Gulf to ensure there is continuous cover in the region while HMS Montrose leaves to undergo routine maintenance.
Mr Hunt said he will add more warships to Britain's fleet if he wins the Tory leadership race and becomes prime minister.
He has vowed to increase defence spending from 2% of GDP to 2.5%, a cost of around £12bn more a year in 2023, and more jets for the navy's new aircraft carriers could be included.
"When you look at this week's events it shows that in recent decades we have run down the navy too much," he wrote in the Daily Telegraph.
Iranian President Hassan Rouhani has previously warned the UK of "consequences" after the seizing of its oil tanker.
Meanwhile, the US is pushing allies to increase their maritime security in the region, safeguarding strategic waters off Iran and Yemen.
Relations between the US and Iran have fractured since President Donald Trump pulled the US out of a nuclear deal with Iran and re-imposed sanctions.