Armed Forces Minister Bob Ainsworth said the seizure at the weekend of the fully-laden oil tanker by pirates 420 nautical miles off the coast of Somalia was of deep concern.
The Foreign Office confirmed that one of the British crew members on board the Saudi-owned Sirius Star is the tanker's chief engineer. The other holds the rank of Second Officer.
"Alongside our international partners, Her Majesty's Government is deeply concerned, not least because two of the crew are British," Mr Ainsworth said, speaking from Kenya.
"Our thoughts are with the men and their families at this difficult time.
"We call on those holding the men to release them and the rest of the crew immediately."
His call came as the US Navy confirmed the vessel, carrying around two million barrels of oil, has anchored off the coast of Somalia near the city of Harardera.
The vessel's operator, Dubai-based Vela International Marine Ltd, said the 25 crew on board - two Britons, two Poles, one Croatian, one Saudi national and 19 Filipinos - were believed to be safe.
A statement from the president of Vela International Marine Ltd, Salah Kaaki, said: "Our first and foremost priority is ensuring the safety of the crew.
"We are in communication with their families and are working towards their safe and speedy return.
"Vela continues to monitor the situation and co-ordinate with the relevant embassies at this time. Vela is awaiting further contact from the pirates in control of the vessel.
"In view of the sensitive nature of this matter and in the interests of the safety of the crew on board, Vela will make no further public comments on this incident until further notice."
The large oil tanker is owned by Saudi oil company Aramco but was sailing under a Liberian flag.
It is 1,080ft long and can carry about two million barrels of oil.
The hijack, which was the first successful attack so far out at sea, raises fears that international patrols nearer the coast and in the Gulf of Aden will not be enough to protect vital trade routes as pirate gangs become ever more audacious.
There were reports today that a Hong Kong cargo ship with 25 crew members on board carrying 36,000 tonnes of wheat bound for Iran has also fallen victim to pirates in the Gulf of Aden.
The Rail, Maritime and Transport union, which represents seafarers, urged the Government to push for expansion of patrolling and escorts to help counter the threat of piracy.
General secretary Bob Crow said: "The growth of piracy is a threat faced by the shipping industry on a global scale and it requires a global response.
"The most important immediate task is to get the Sirius Star, and the many other vessels already being held by pirates, released with their crews unharmed.
"Like all workers, seafarers should be able to work without the fear of imminent attack, and the ordeal faced by seafarers held to ransom is unimaginable.
"The scale of the problem is now so big that the Gulf of Aden, where so many seizures have taken place, is known among mariners as the 'gates of hell'.
"One problem is that some ship owners, particularly those flying flags of convenience, will gamble with their crews' safety by taking short cuts outside the patrolled safe zone."
Saudi Foreign Minister Prince Saud, speaking in Athens, called the hijacking "an outrageous act".
He added: "Piracy, like terrorism, is a disease which is against everybody, and everybody must address it together."
Spokesmen for both Nato and the US Navy said they did not have any plans to intercept the ship.
Cyrus Mody, manager of the International Maritime Bureau - a specialised division of the International Chamber of Commerce - said it was very difficult for security patrols to intervene once a ship had been boarded.
"Once the pirates are on a vessel, you have the risk of the crew being used as human shields or being injured in crossfire.
"There could also be damage to the ship's cargo and very often they carry a mixed cargo - some hazardous, some not - so it is a very difficult judgment call."
The renewed fears about piracy came as it was announced today that eight suspected Somali pirates were handed over to the Kenyan authorities by the Royal Navy following an attempted hijacking in the Gulf of Aden last week.
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