A ship has run aground off the Italian coast, killing two French passengers and a Peruvian crew member.
The AFP news agency is reporting that 50 passengers are still missing as divers search the stricken vessel. Fourteen people have been injured.
According to the British consulate in Italy, 25 British passengers were on board, as well as 12 British crew members. All have been accounted for as safe.
The ship hit an object - thought to be a rock - near to the Tuscan island of Giglio. Having taken on water, it listed before resting half-submerged at an angle on the sea floor.
An evacuation operation involving five helicopters, from the coast guard, navy and air force, as well as boats and divers was launched after the luxury liner began to capsize. More than 4,000 people were rescued, though the search continues. Those pulled from the water are being sheltered in hotels, schools and churches on the island.
According to the Press Association, British consular staff have been dispatched to the scene of the incident. One British passenger on board the liner told her father the incident "felt like the sinking of the Titanic".
The BBC reported that Dancer Rose Metcalf, 22, who had been working on the ship, was winched to safety by a helicopter after it ran into trouble. "The ship had rolled on its side so she was ready to jump in the water," he said
In a statement on its website, the cruise company Costa said: "Costa Cruises confirms the evacuation of about 3,200 passengers and 1,000 crew members on board of the Costa Concordia.
"An incident occurred near the island Isola del Giglio of the coast of Italy. The evacuation started promptly, but the position of the ship has worsened, making it more complicated to complete the last part of the evacuation. At this moment, the cause of the incident cannot yet be confirmed."
Reports suggest there were around 1,000 Italians on board, as well as 500 Germans, 160 French and more than 1,000 crew members. The Mediterranean cruise was en route to Savona, with further stops scheduled for Marseille, Barcelona, Palma de Mallorca, Cagliari and Palermo.
"Our first thoughts go to the victims and we would like to express our condolences and our closeness to their families and friends," said Costa.
"In this moment all our efforts are focused on the completion of the last emergency operations, besides providing assistance to the guests and the crew who were onboard."
According to the Italian news agency Ansa, some people had jumped overboard in the scramble to leave the ship, which is said to have hit an obstacle around three hours after it begun its voyage from the port of Civitavecchia.
The cruise company added: "We would like to express our profound gratitude to the coast guard and all the forces co-ordinated by the coast guard, who have been involved in the rescue and assistance to guests and crew members.
"The company will fully co-operate with the relevant authorities in order to determine the causes of what happened."
Reported by the Press Association, Fabio Costa, an employee on the ship, said people were jumping into the sea to swim ashore.
Speaking to the BBC, he described the terror as the boat began to list: "We were all working and all of a sudden we felt the boat hitting something and everything just started to fall, all the glasses broke and everybody started to panic and run.
"We could only feel that the boat had hit something, we had no idea how serious it was until we got out and we looked through the window and we saw the water getting closer and closer. Everything happened really, really fast and we saw the water coming in."
"A lot of people were falling down the stairs and were hurt because things fell on them," he added.
Costa said he saw a huge rock, which is probably what the vessel struck.
"People were having huge trouble trying to get on the lifeboats. So at that point we didn't know what to do so it took hours for people to get off the ship.
"It was easier for people to jump into the sea because we were on the same level as that water so some people pretty much just decided to swim as they were not able to get on the lifeboats."
The Foreign Office gave contact details for the British Embassy in Rome for concerned friends and relatives. The telephone number is (+39) 06 4220 0001, and the Foreign Office in London can be contacted on 0207 008 1500.
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