Minister Maurizio Lupi retweeted a post from local media putting the death toll at eight, with 427 rescued.
The Italian coast guard earlier said that all remaining passengers had been evacuated from the vessel, with the boat's commander finally leaving the ship at 2:50 p.m. Monday. The coast guard told CNN it was inspecting the ship and deciding how to transport it -- and where.
More than 400 passengers had been traveling on the Norman Atlantic between the Greek port of Igoumenitsa and the Italian port of Ancona when the blaze broke out in the ferry's parking bay.
In the first three hours of the fire, around 150 people were able to escape via the vessel's lifeboats. But when the ferry lost power, the electronic arms were unable to function, leaving the rest of the boats dangling uselessly by its side.
Rescue efforts were hampered by strong winds, choppy seas and thick smoke, which prevented other boats from getting close enough to the vessel to get people off.
After waiting for hours in rough conditions, one Greek man told Italian state broadcaster RAI TV that passengers were "dying of cold and suffocating from the smoke," and that their feet were "burning" from the heat of the flames.
Helicopters with night vision equipment worked through the night to pull passengers off the ferry, one by one.
An Italian navy medical team boarded the ship to aid passengers, some of whom had been suffering hypothermia and smoke inhalation, the navy said. The already cold conditions were worsened by the spray from tugboat hoses as authorities attempted to douse the flames.
By Monday afternoon, the Italian navy said 419 people had been rescued, with the country's coast guard later confirming that no passengers remained on board.
A freighter carrying 49 rescued passengers arrived at the port of Bari, Italy, on Monday. Photos showed survivors wrapped in emergency foil blankets being carried away on stretchers.
Greek Merchant Marine Minister Miltiades Varvitsiotis earlier raised the death toll to five.
One man died after he jumped or fell into the cold water, authorities said. It is unclear how the other four victims died.
Dramatic cell phone images filmed by a passenger showed flames through shattered portholes, while a wider view released by rescuers showed a huge plume of thick, black smoke streaming from the stricken vessel.
Many passengers were unable to reach the lower decks because of the heat, and the water below was so cold that jumping clear of the ferry was not an option.
Sea surface temperatures had been around 14 to 15 degrees Celsius (57 to 59 degrees Fahrenheit), CNN meteorologist Tom Sater said, which would have limited the survival time in the water to six hours at most.
Passengers told Greek and Italian newsgroups they had felt like "prisoners on a burning ship."
It's not known how the fire started, but it's believed to have originated in the parking bay. A truck driver told the Greek news media that trucks filled with oil were "packed like sardines," their cargo scraping the ceiling, which could have set off sparks in rough seas to start a fire, he surmised.
Greek authorities said the vessel's fire doors appeared to have failed, which allowed the flames to spread quickly.
The disaster made national headlines in Greece, Italy and other countries with citizens aboard the ferry. In a Sunday morning public address, Pope Francis offered "affection and prayers" to those affected by the Norman Atlantic ferry fire as well as a collision in the Adriatic Sea between two merchant ships.
