The coach bringing 46 children and four teachers back to Belgium from a skiing holiday hit a concrete wall late Tuesday in the motorway tunnel near the town of Sierre.
A total of 22 children from two Catholic primary schools were killed, along with the teachers and both coach drivers, and 24 reported injured.
The injured, three of whom were said to be in a coma, were taken by ambulance and helicopter to four hospitals as fire crews worked for hours to cut them free from the twisted wreckage of the coach.
Belgium announced a day of national mourning, while the Swiss parliament observed a minute's silence for the victims.
Belgian Prime Minister Elio Di Rupo and Swiss President Eveline Widmer-Schlumpf were due to visit the site of the crash later on Wednesday.
"This is a tragic day for all of Belgium," said Di Rupo.
As well as Belgians, the children included 10 of Dutch nationality and one Pole, authorities said.
Police in the southern Valais canton told reporters early on Wednesday that the tragedy was "unprecedented" and that even seasoned rescuers had been traumatised.
Surgeon Jean-Pierre Dellars said in one of the hospitals: "All the rescuers were shocked by what they have experienced."
The injuries were so bad that the death toll could well rise, he added.
The coach, in a convoy of three hired by Catholic education authorities in Belgium's Flanders region, carried pupils from primary schools in Lommel, near the Dutch border, and Heverlee, in the suburbs of Leuven in the centre.
"The magnitude of the accident is difficult to digest ... for the moment I am concentrating on the practical aspects," said Belgium's ambassador in Switzerland Jan Luykx who visited the accident site early on Wednesday.
"The emotional side will come when we meet with the families," he added.
Belgian authorities said were doing everything they could to ensure that the families of the victims were kept informed and treated with dignity, the prime minister's office said.
But at Heverlee parish priest Dirk de Guedt said the parents did not know which children had been killed and which had survived.
Of the 22 children from the 't Stekske school in Lommel, five had phoned their parents but there was no news of 17 others, deputy mayor Kris Verduyckt was quoted as saying by Belga news agency.
"I'm at a loss for words," Transport Minister Melchior Wathelet told RTBF radio. "Terribly hurt, terribly moved.
"We are all thinking like parents, with this terrible thought for the those parents who will not see their children coming back today," he said.
"Yesterday evening, they were looking forward to seeing them and they won't see them again."
It was unclear what caused the bus to swerve to the right, mounting the kerb before hitting a concrete wall at the end of an emergency lay-by. The accident happened between the east and west exits for the city of Sion.
Belgian transport company Toptours operated the 2002-registered coach and had an "excellent reputation," said Wathelet.
"It has always respected the rules," regarding safety, he added.
The bus was towed for examination to a cantonal police depot close to the site of the accident early on Wednesday.