Twenty-three people were rescued from the wreckage while operations continued overnight and into Sunday morning to find the missing - the plane's technician and another person whose identity was not known - off the northwestern coast of Sicily.
Remains of the ATR-72 plane, which was flying from the southern Italian city of Bari to the Tunisian resort of Djerba when it crashed, were towed into port in Sicily overnight, but the aircraft's nose and tail sank to the sea floor.
Admiral Vicenzo Pace, the commander of the Palermo harbourmaster's office, said 13 people were confirmed dead among a total of 38 people on board. The authorities had earlier said 39 people were on board.
The cause of the crash was not immediately known but the pilot had reported engine trouble, and the Italian transport ministry ruled out an attack.
Rescuers had yet to retrieve the black box from the plane, a charter aircraft operated by Tuninter, a subsidiary of the national carrier Tunisair, the Palermo harbourmaster's office said.
All 34 passengers were Italians, and the four crew were Tunisians, two of whom survived.
Two children, aged 2 and 8, were among the victims.
"I saw the baby die. He was in his mother's arms, but the sea just tore him away from her when we fell, and we were flung into the water," one survivor, 23-year-old student Illaria Le Bosco, told La Repubblica newspaper.
A chartered aircraft arrived in Palermo from Bari overnight, carrying the families of the Italian victims and survivors, most of them young couples from the southeastern Puglia region.
The French-built ATR-42 had passed
four inspections (file photo)
Eleven survivors were being treated at the Civico hospital in Palermo, according to Toto Cuffaro, the head of Sicily's regional council, who visited the hospital.
"It's a miracle we are alive," Addolorata De Pasquale told the Italian news agency Ansa. Some of the survivors were fished out of the water, while others clung to the wings of the wreckage.
Tales of survival
Sunday's Italian press carried poignant interviews with the victims' families and friends, as well as tales of survival.
Three couples from Modugno in southeastern Italy, heading to Tunisia at the busy start of the Italian summer holiday period, perished together in the crash.
"They decided to go to Djerba at the last moment, after the attacks in Sharm al-Shaikh," the Egyptian Red Sea resort where bombings killed 67 last month, a friend told Ansa.
One survivor, 25-year-old Gianluca La Forgia, said in hospital how he and his girlfriend had been able to get out of the plane via a hole smashed in the fuselage by the impact with the water.
"It was like being in a film," he said.
According to initial reports from the plane's pilot, who was injured in the crash, the aircraft lost power, causing it to hit the water at a steep angle.
The pilot had reported engine problems shortly after take-off and had intended to make an emergency landing at Palermo. When that proved impossible, he brought the plane down on the sea about 33km from Palermo off Sicily's northern coast.
Luciano Lucarelli, who was rescued with his fiancee, said one of the plane's two turboprop engines had failed and its propeller had blocked.
"Then the other propeller stopped, and the plane started going down steeply," he said.
The French-built plane, delivered in 1992, had passed four inspections, the last on 25 March at Catania, Italian and Tunisian aviation authorities said.
ATR, which dispatched a two-man team to the scene on Sunday, has promised to cooperate in the investigation that will be carried out by the Italian and Tunisian authorities, with support from the French.