Rescuers have been through almost all of the ship that remains above the water line and experts believe there is little risk of a major fuel leak.
Eleven bodies have been recovered so far and 24 people are missing.
The captain of the Italian ship, Francesco Schettino is under house arrest, accused of causing the crash.
The firm says this could take several weeks.
The announcement that Captain Francesco Schettino would be held under house arrest instead of in jail came as prosecutors accused him of causing the crash and also of fleeing the Costa Concordia while passengers were still stranded.
A recording of a call between him and a port official after the crash appears to support this, though Captain Francesco Schettino denies the claims.
In the recording, released by the Corriere della Sera newspaper, Livorno Port Authority chief Gregorio de Falco can be heard repeatedly telling the captain to get back on board the ship to help the stranded passengers.
“Schettino, maybe you saved yourself from the sea, but I’ll make you have trouble for sure. Go aboard,” says Gregorio De Falco.
Francesco Schettino appears to refuse, replying first that there are rescuers already on board, and then that it is dark and difficult to see.
Gregorio De Falco replies: “Do you want to go home, Schettino? It’s dark, so you want to go home?”
Coastguards believe Captain Francesco Schettino never went back to the ship. He was arrested shortly afterwards.
But during a court hearing on Tuesday, the captain said he could not get on board the vessel because it was lying on its side.
Francesco Schettino argued that after hitting rocks he had executed a difficult manoeuvre that had saved many people’s lives.
The ship, carrying 4,200 passengers and crew, had its hull ripped open when it hit rocks late on Friday, just hours after leaving the port of Civitavecchia for a week-long Mediterranean cruise.
Some people were forced to swim for shore as the angle of the ship made launching lifeboats impossible.
Lloyd’s List said that the vessel passed within 230m of the island on 14 August 2011 to mark La Notte di San Lorenzo – the night of the shooting stars festival on the island.
The route deviation on that occasion had apparently been authorized by Costa Cruises – the company which owns the vessel.
The company said on Monday that the ship was never closer than 500 m to the coast when it passed on 14 August.
Lloyd’s List describes that occasion as a “near miss” and says the ship’s route would have been less than 200 m away from the point of collision on Friday’s voyage.
Costa Cruises said on Monday that the route deviation last Friday had been “unauthorized, unapproved and unknown to Costa”.
But Richard Meade, the Editor of Lloyd’s List, said: “The company’s account of what happened, of the rogue master [Capt Schettino] taking a bad decision, isn’t quite as black and white as they presented originally.”
“This ship took a very similar route only a few months previously and the master would have known that.”
Costa Cruises says it is looking into the claims, but stands by the statement it gave on Monday.
Meanwhile, Lloyd’s List says the issue of which nautical charts the captain of the vessel was using looks likely to be critical to his defense if he does face a criminal prosecution.
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