According to officials, four men and a woman were found on the ship, which capsized after it hit rocks in Ialy on Friday.
Judges are questioning the ship’s captain, Francesco Schettino, who has been blamed for steering the vessel on to the rocks.
Captain Francesco Schettino has been detained on suspicion of manslaughter, but denies any wrongdoing.
He has not yet been formally charged, but prosecutors on Tuesday asked judges to continue his detention.
In the recording, on the Corriere della Sera’s website, Captain Francesco Schettino appears to refuse to go back on to the ship to co-ordinate the rescue effort.
A man who identifies himself as 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.
Captain Francesco Schettino is heard replying first that there are rescuers already on board, and then that it is dark and difficult to see.
Shortly after daybreak on Tuesday rescue crews blasted several holes in the ship, now lying on its side metres from Giglio island, in order to gain access to areas they had not yet been able to search.
Hours later, the coast guard announced that more bodies had been found.
It is not clear whether the bodies are crew members or passengers, but the coast guard said they were aged between 50 and 60 and were wearing life vests.
The bodies were found near one of the assembly points where people were told to gather in an emergency.
Before the bodies were discovered, Italian officials said there were 29 people still missing from the vessel.
Teams of specialist divers have been helping with the rescue mission, but they have been hampered by bad weather.
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.
Francesco Schettino, 52, has emerged as the central figure in the investigation.
The Costa Concordia’s owners, Costa Cruises, have said Captain Francesco Schettino hit the rocks because he deliberately steered the ship towards Giglio Island.
Prosecutors have given more detail, saying the captain wanted to make a close pass of Giglio in order to “salute” a crew member’s family who lived there.
On Monday, the shipping newspaper Lloyd’s List said it had been able to trace the course of the Costa Concordia though 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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