The radio report said 11 people were hospitalised with injuries, two of them in critical condition. It was not immediately known if there were other survivors or any missing. Four children are among the rescued.
"Looking down from the overpass, the scene of the tragedy: Some 30 bodies covered by white sheets, lined up along the roadside," said Cesare Abbate of Italy's Ansa news agency. From time to time, rescue workers called for "a moment of silence" to listen for signs of life from the wreckage, he said.
Flashing signs near Avellino, outside Naples, had warned of slowed traffic ahead along a stretch of a major highway crossing southern Italy, before the crash occurred, said highway police and officials. It was not immediately clear why the bus driver lost control of the vehicle. Some reports suggested the bus had had a brake failure as it entered the flyover.
A reporter for Naples daily Il Mattino, Giuseppe Crimaldi, told Sky TG24 TV from the scene that some witnesses told him the bus had been going at a "normal" speed on the downhill stretch of the highway when it suddenly veered and started hitting cars.
He said some witnesses thought they heard a noise as if the bus had blown a tyre.
The driver steered into the concrete barrier to avoid any further collisions, only for the barrier to give way. Ansa said the driver's body would be examined for the possible presence of alcohol or drugs.
Hours after the crash, firefighters said that they had extracted 37 bodies. Most of the dead were found inside the mangled bus, which lay on its side , while a few of the victims were pulled out from underneath the wreckage, Ansa reported.
One car's rear was completely crumpled, while another was smashed on its side. It was not immediately known if anyone in those cars had been injured.
Early reports said the passengers had spent the day in Puglia, an area near the Adriatic on the east coast famed for religious shrines. But later, a state radio reporter at the scene said authorities told him that the bus had been bringing the passengers home after an outing to a thermal spa area near Benevento, a town not far from Avellino.
Others at the scene said the passengers might have visited another nearby town, Benevento, which was the early home of Padre Pio, a late mystic monk popular among Catholics in Italy. Passengers came from small towns near Naples, and relatives streamed to the crash site.