Prosecutors say Francesco Schettino caused the accident through negligence, and then fled the Costa Concordia while passengers were still stranded.
A recording of a call between Captain Francesco Schettino and a port official shortly after the crash appears to support some of the prosecutors’ accusations.
Captain Francesco Schettino denies the claims.
The local authority says 20 passengers are still missing. They include people from Germany, Italy, France and the US.
Four crew members – one each from Italy, Hungary, India and Peru – are also missing.
“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 he never went back to the ship. He was arrested shortly afterwards and has been held in jail since.
But during a court hearing on Tuesday, Francesco Schettino said he could not get on board the vessel because it was lying on its side.
He argued that after hitting rocks he had executed a difficult manoeuvre that had saved many people’s lives.
Prosecutor Francesco Verusio, who had argued that Captain Francesco Schettino was a flight risk, said he did not understand the ruling.
“I’m keen to read the reasoning,” he said.
Meanwhile, rescuers found six more bodies in the wreck of the ship on Tuesday, bringing the confirmed death toll to 11.
“The five victims are a woman and four men, who could be passengers, but we are not sure,” said coastguard spokesman Filippo Marini.
He added that the dead people were between 50 and 60 years old, and were wearing life-jackets.
The bodies were found near one of the assembly points where people were told to gather in an emergency.
The authorities are also battling to avoid an environmental disaster, amid fears that the cruise ship’s fuel tanks could break apart and shed thousands of tons of diesel into the sea.
Specialist salvage teams have been drafted in, and are due to start pumping the fuel out in the coming days.
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.
Infrared footage taken from a helicopter showed lines of people climbing ropes down the exposed hull of the vessel to reach rescue boats on the water.
On Monday, the shipping newspaper Lloyd’s List said it had been able to trace the course of the Costa Concordia through information from satellites.
Lloyd’s List issued a graphic comparing Friday’s sailing with an earlier sailing by the vessel, suggesting that Friday’s route had deviated far from its usual course.
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