The impact of the crash was so severe some people were thrown from the vehicle and killed.
Other badly burned bodies were pulled from the wreckage, police said.
The bus was carrying Hungarian teenage students back from France to Budapest when the driver lost control and it hit an overpass support column on the A4 near Verona in Italy.
Thirty-nine people survived the crash but 26 were injured, 10 seriously, and emergency services fear the number of fatalities could increase.
Hungarian Foreign Minister Peter Szijjarto said: “One passenger is currently in an induced coma and in life-threatening condition.”
Italian news agency Agi suggested the French bus driver and his family could be among the victims.
RAI state radio said a Slovenian lorry driver travelling behind the bus had noticed a problem with one of the wheels and attempted to alert the driver.
Police commander Girolamo Lacquaniti said it was not clear why the bus had hit the barrier just before midnight on Friday.
He added that there had been no other vehicles involved.
Parents of some of the children, all aged between 15 and 17, involved in the accident had travelled to the scene of the accident on Saturday afternoon.
Outside the school in Budapest, 60 students gathered for a vigil, lighting candles and laying flowers.
One of them, Tamas Mezo, said: “We knew many of them. I was very much planning on going this year but in the end it didn’t work out.
“There were three or four teachers on the bus and unfortunately one of them did not survive. Our hearts are hurting because we loved him and he was really nice.”
Footage of the burnt out wreckage from the Italian fire service showed the severity of the fire.
The foreign ministry in Budapest said official information showed there were 54 passengers on the bus, including teachers accompanying the students and two drivers.