At least one person died and two were injured in the risky rescue operation.
The Italian navy said 251 of the 478 people on the ferry, sailing from the Greek port of Patras to Ancona in Italy, had been evacuated by early Monday.
Most were airlifted by helicopter to other merchant vessels sailing nearby, though a few were flown to hospitals in southern Italy to be treated for hypothermia.
Greek Merchant Marine Minister Miltiadis Varvitsiotis said 10 merchant ships were in the area assisting rescue efforts, and that those which had already taken on dozens of passengers from the stricken ferry would remain in the area until the operation was over. Only then would it be determined where they would go, Varvitsiotis said.
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Nevertheless, officials in the Adriatic port of Bari were preparing for the first large group to arrive Monday - some 49 people. They were initially expected in Brindisi down the coast, but rough seas forced a change of plans, officials said.
"We are outside, we are very cold, the ship is full of smoke," passenger Giorgos Stiliaras told Greek Mega TV.
He recalled people being awakened by "the smell of burning plastic" and that the heat from the fire felt like the floors were "boiling."
Dotty Channing-Williams, mother of ferry passenger Nick Channing-Williams, said she had managed to speak to her son before he and his Greek fiancee were airlifted to safety.