The toll included the bodies of two women, their nationalities so far unknown, found by divers on deck number four Monday.
So far Italian prosecutors have focused on Captain Francesco Schettino, who is accused of causing the accident and is under investigation for multiple manslaughter and abandoning the 450 million euro ship before it was evacuated.
Schettino's lawyer said that evidence from his client about phone calls with the ship's owners, Costa Cruises, at the time of the accident, could lead to the investigation being widened.
Schettino's phone calls with the owner's marine operation director "... have opened further channels for investigation that could reasonably lead to an increase in the number of those under investigation," his lawyer, Bruno Leporatti, said in a statement.
Third parties "could have at least contributed to creating the tragic event," Leporatti said.
According to leaked transcripts from the investigation, Schettino has admitted steering too close to shore and Leporatti has said that while Schettino is willing to accept his share of responsibility, other factors were also involved in the accident.
Investigators say he brought the ship to within 150 meters of the shore, apparently while performing a "salute" to the island, a maneuver which Schettino says was common but which the company says could not be performed so close to the shore.
Costa Cruises, a unit of Carnival Corp, the world's largest cruise ship operator, has suspended Schettino and declared itself an injured party in the case. It has said "unfortunate human error" by Schettino was the cause of the disaster.
Neither Marco De Luca, a lawyer representing Costa Cruises, nor spokesmen for the company in Genoa and in London were immediately available for comment.
According to transcripts of Schettino's questioning by prosecutors leaked to Italian media Saturday, the captain said that immediately after hitting the rock he sent two of his officers to the engine room to check on the state of the vessel.
As soon as he realized the scale of the damage, he called Roberto Ferrarini, marine operations director for Costa Cruises.
"I told him: I've got myself into a mess, there was contact with the seabed. I am telling you the truth, we passed under Giglio and there was an impact," Schettino said.
"I can't remember how many times I called him in the following hour and 15 minutes. In any case, I am certain that I informed Ferrarini about everything in real time," he said.
What Schettino alleges that Ferrarini responded has not yet been made public.
Separately, Leporatti said that Schettino tested negative in hair and urine tests for drug use, but was not tested for alcohol on the night of the accident.
If the probe is broadened, it will reduce the glare of the spotlight on Schettino, who has so far been assigned almost exclusive responsibility for the disaster, though his first officer Ciro Ambrosio is also under investigation.
A judge has said Schettino showed "incredible carelessness" and a "total inability to manage the successive phases of the emergency," according to documents from a hearing.
Search operations were still under way for nearly 20 bodies missing in the waters off the island of Giglio.
The possible presence of unregistered passengers, including one Hungarian woman, has made it difficult to know the exact number of people missing. Costa Cruises denies that there were unregistered people on board.
Franco Gabrielli, head of Italy's civil protection authority, said the ship was stable and there appeared no immediate risk that it could slide off the rock outcrop where it is caught and slip into deeper waters.
He said search operations could continue and operations to pump some 2,400 tons of fuel from the vessel could begin while the search for bodies was still under way.
Navy divers blasted new underwater holes in the hull of the ship to provide additional points of access. Debris floated out and was gathered by coastguard boats.
An Italian navy ship, the Galatea, which is equipped with a sophisticated undersea radar system, has been sent to the area to help search for bodies.
The greatest fear of the island's 950 permanent residents is an ecological disaster that pollutes the pristine waters.
Giglio's economy depends on tourists seeking clean beaches and clear water for snorkeling and scuba diving. Its drinking water, too, is drawn from the sea and desalinated.
SMIT, the Dutch company hired to salvage the fuel, has said it is ready to begin extraction operations as soon as it receives the go-ahead from authorities