The mass of flowers, candles and messages for the victims of Friday's tragedy continued to grow outside the children's school in central Budapest.
A national day of mourning has been set for Monday, while a probe of the crash into a bridge pillar near Verona revealed no traces of braking prior to the collision.
Some victims were catapulted out on impact but mostly they perished inside. Those who escaped did so by desperately smashing windows and leaping out.
Several hundred people stood in silence outside the pupils' school, Pal Szinyei-Merse secondary, on a freezing Saturday night to pay their respects as hundreds of tiny candle flames flickered.
"Even though I graduated from the school five years ago, I spent many happy years here," said Timea Deutsch, 24. "It's tragic."
Of the 56 people on board 28 were injured, Italian police said. Six, all adults, remained in hospital including two in a critical condition, Hungary's consul said late Saturday.
The government said flags would fly at half-mast outside parliament on Monday as part of the day of mourning.
"Black flags will be hung on public buildings and schools should find a way to mourn the victims of this accident with dignity before and after classes," it said.
Cardinal Peter Erdo called on worshippers to remember the victims at church services around the country.
"I am praying for the unfortunates who died and for the swift recovery of the injured," Erdo said in a statement.
Foreign Minister Peter Szijjarto said Sunday that the victims were so badly charred that it may take several days yet to identify them all. He said that the repatriation of the injured could start Sunday.
Hungarian police meanwhile announced Sunday the start of their own enquiry parallel to the investigation by the Italian authorities.
Tibor Czako, head of the Pizolit company that owned the bus said it was "in good condition" and "road-ready" before the crash.
Verona traffic police chief Girolamo Lacquaniti had said Saturday that no other vehicle was involved, which suggested mechanical or human error was the cause.
"The coach was travelling at quite a constant speed and we haven't found any traces of braking," Lacquaniti said on Italian radio. One of the two drivers on board was among those killed, Italian media reported.
Judit Timaffy, Hungary's consul, said that the death toll could have been worse were it not for a teacher, who went back on the bus to bring children off. He was thought to be one of those seriously injured and Italian press reports said his son and daughter were on the coach.
The son may have survived but his sister is thought to be dead, the reports said.
Hungarian Prime Minister Viktor Orban on Saturday expressed his horror and shock in a statement carried by state news agency MTI.
"At this time of mourning I am praying and am with the families and loved ones of those affected by this tragedy," Orban said.
Russian President Vladimir Putin, with whom Orban enjoys good relations, also expressed his condolences.
"It is especially tragic that children and teens became the victims of the accident," Putin wrote, according to a Kremlin statement.