The Italian navy, which has been coordinating efforts to winch people of the Norman Atlantic by helicopter, said a total of 335 of the 478 passengers and crew had been taken off the boat, which continued to be buffetted by powerful, bitingly cold winds and huge waves.
The Italian-owned ship, which was travelling from Patras in western Greece to Ancona in Italy, has been drifting off the coast of Albania since a fire ripped through its car deck in the early hours of Sunday, leaving it impossible to steer.
A flotilla of merchant, coastguard and military ships from Greece, Italy and Albania have been involved in what has proved to be a fiendishly difficult evacuation operation.
The drama has claimed one life so far, a Greek passenger who fell into six-metre high waves while trying to get into a lifeboat on Sunday. His wife also ended up in the sea but was rescued.
Some of the rescued passengers have displayed symptoms of hypothermia and there were fears those still on board would be worse-affected.
A medical team was on board the ferry helping to decide who should be given priority for evacuation. The multinational crew, headed by Italian skipper Argilio Giacomazzi, 62, were expected to be the last off, in keeping with maritime tradition.
Underlining the challenges posed by the continuing bad weather, the merchant ship "Spirit of Piraeus", which had picked up 49 of the evacuees, was unable to dock at the Italian port of Brindisi on Monday, opting instead to head to a bigger container port further up the coast at Bari.
The group included 20 Greeks who were expected to be flown home on a C-130 military transport plane dispatched to Lecce on Italy's southeastern heel.
Among those evacuated to hospitals near the city were a two-year-old Swiss boy, his four-year-old sister and their seven-month-pregnant mother.
In desperate scenes on Sunday, terrified passengers pleaded by mobile phone to be saved from the vessel, which was travelling from the Greek port of Patras to Ancona in Italy.
"I cannot breathe, we are all going to burn like rats - God save us," cried one of the ship's cooks.
Italian authorities have mobilised four tugs to bring the "Norman Atlantic" to port - either in Italy or Albania - once the evacuation has been completed.
The miserable conditions on the exposed top deck and the bridge of the ship were recounted by passengers to Greek television stations.
"We are on the top deck, we are soaked, we are cold and we are coughing from the smoke. There are women, children and old people," passenger Giorgos Styliaras told Mega TV.4
Another told the station that "our shoes were melting" from the heat of the fire shortly after it first broke out.
The Greek maritime ministry said 268 of the passengers on the ferry were Greek, with the crew made up of 22 Italians and 34 Greeks.
The rest of the passengers included 54 Turks, 44 Italians, 22 Albanians, 18 Germans as well as Swiss, French, Russian, Austrian, British and Dutch nationals.
The "Norman Atlantic" left Patras at 1530 GMT on Saturday and made a stop at the Greek coastal town of Igoumenitsa, before heading to Ancona when the fire took hold.
The car deck of the Italian-flagged ferry, built in 2009, was believed to have been holding 195 vehicles, including more than 20 tankers carrying olive oil, when the fire broke out.
Questions were now expected to be asked about why the fire was not contained.
Carlo Visentini, the chief executive of the Visenti Group which owns the boat, said the vessel underwent checks on December 19 in Patras and the minor flaws revealed had been addressed, including a problem with a fire door.
"This was immediately repaired to the satisfaction of the inspectors," he said.