Corriere named the Italian victims as Valentina Gallo, Elena Maestrini, Serena Saracino , Francesca Bonello, Elisa Valent, Lucrezia Borghi and Elisa Scarascia Mugnozza.
Saracino, from Turin, died of her injuries on Monday morning. Her father was quoted by Huffington Post Italia as saying: "She was a long-haired angel. She loved Barcelona but it cost her her life, and killed her mum and dad too."
The victims of Sunday's crash, all aged between 19 and 25, also included a Romanian, a Frenchwoman, an Austrian and a student from Uzbekistan, Jordi Jane, who heads up interior matters for Catalonia, said on the radio.
"Some of them were not wearing seat belts," Jane said.
The bus was carrying students from about 20 countries, many of them on a European exchange programme in Catalonia.
Dozens were injured when the driver lost control of the coach and crashed into an oncoming car near the small town of Freginals as the group returned from a festival.
The driver, who was questioned by police Sunday, is in intensive care being treated for chest injuries, Jane said. He was due to appear before a judge on Monday, but the hearing has been postponed, a legal source told AFP.
The accident occurred about 150 kilometres (95 miles) south of Barcelona as the students were returning from the Fallas festival in eastern Valencia, known for the burning of giant statues.
In a message on its website on Sunday, the Foreign Ministry confirmed Italians were among the dead, but did not say how many.
Annalisa Riba, 21, from Turin, was among those injured, La Stampa reported.
Five other Italian students from Turin Polytechnic had also attended the festival, but returned to Barcelona on a bus that left before the one that crashed.
"We bought tickets for the last four seats," 23-year-old Lorenzo Eula told La Stampa.
"There were many Italians at the departure point, also among the organizers. We only heard about the accident over the internet, a friend received a WhatsApp with a link to an online story."
Prime Minister Matteo Renzi said on Twitter he was "heartbroken" over the deaths.
Six of the more than 30 injured were in a critical condition in hospital.
The bus driver "hit the railing on the right and swerved to the left so violently that the bus veered onto the other side of the highway," said Jane.
The bus then hit a car coming in the opposite direction, injuring two people inside, he added.
Spain's Interior Minister Jorge Fernandez Diaz, who went to the scene, said it was still not clear why the bus driver hit the railing in the first place, adding however that the accident was likely due to a "human factor".
An AFP photographer at the scene several hours after the crash said many fire engines were there, as were three hearses and a heavy-lift crane.
The car's front was smashed in, and the bus was lying on its side after the accident.
It was eventually lifted onto a truck and driven away - its windscreen smashed and the back part of its roof caved in.
Jose Roncero Pallares, the mayor of Freginals, said the accidents that had hit that stretch of the motorway over the past years had always taken place in the area where the crash happened.
"I don't know why, the highway looks fine and it's a straight line," he told AFP.
"It rained a lot that night and maybe that played a role."
Catalonia's high court said in a statement that an initial probe revealed "the bus driver tested negative for drugs and alcohol".
Minutes of silence
The accident is one of the deadliest in Spain in recent years.
In November 2014, a bus carrying pilgrims fell into a ravine in the southeast of the country, leaving 14 dead and another 41 injured.
Spain's Prime Minister Mariano Rajoy tweeted his concern on Sunday.
"My condolences to the families of the victims and I wish rapid recovery to the injured," he wrote.
Catalonia's newly-elected regional president Carles Puigdemont, meanwhile, visited the area after cancelling a planned trip to Paris.
Joining in mourning for the tragedy, players for Barcelona and Villarreal - which is only around 100 kilometres (62 miles) from the crash site - observed a moment of silence before kick-off, as will those from the Real Madrid and Sevilla later Sunday.