The aircraft, which was flying from the southern Italian city of Bari to the Tunisian resort of Djerba, plunged into the water northwest of the Italian island of Sicily on Saturday.
It was carrying 34 passengers, all believed to be Italians, and five Tunisian crew members.
The pilot, who survived the crash, radioed for help after the engines lost power and made a forced landing about 33 km from Palermo.
Rescuers saved 23 of the 39 people on board, but were still searching for three missing – two of whom were believed to be crew members.
One official said recovering the bodies might be difficult because they could be trapped inside part of the plane that was still submerged.
Emergency crews were also searching for the flight data recorder.
Some survivors said the engines had gone silent seconds before the crash and they barely had time to put on their life jackets before impact.
They spoke of chaos inside the cabin of the Tuninter ATR-72 and of swimming through debris and dead bodies to get to safety.
“I took a breath of air and then I felt the water rushing onto me,” Passenger Roberto Fusco told The Associated Press. “I took off my seat belt and was able to make my way to the surface.”
Officials said the plane had been in service for about 13 years and had passed a check in March.
Recovery workers hauled the aircraft’s mangled fuselage out of the sea on Sunday, its two wings intact.
Investigators were relying on the two turboprop engines to find what caused the crash.
“The breakdown of both engines is a completely atypical occurrence,” the head of Italy’s civil aviation agency, Commander Silvano Manera, said.
He said an analysis of the fuel put in the plane’s tanks before takeoff did not detect impurities. One possibility was a fuel tank leak, he said.
“All hypotheses are open, except that of sabotage,” he said listing a technical breakdown, weather factors, structural defects, operational problems and human error as possibilities.
Italian authorities ruled out a possible terrorist attack.
Italian Transport Minister Pietro Lunardi called for tougher standards for charter planes, saying existing controls needed to be reinforced.