The extent of the catastrophic fire on New Year's Eve cannot yet be fully assessed.
"40 people" have lost their lives, according to Mathias Reynard, regional director of the canton of Valais, but the death toll is feared to be higher.
The number will change in the coming hours and days.
A total of 119 people are being treated in hospitals, around 50 of them outside Switzerland, including in France, Italy and Belgium.
Not all the dead have been identified, and that work is believed to be ongoing for weeks.
"Our priority is to identify the deceased, so that relatives can mourn their dead," said the canton's chief prosecutor, Beatrice Pilloud.
Painstaking work
While remains have begun to arrive at the funeral centre in the nearby city of Sion, identification work is underway, including using DNA samples and possible characteristics of the victims, says police chief Pierre-Antoine Lengen.
"It's a complicated process. We can't afford to make any mistakes."
Many foreign nationals are believed to be among the victims, but not all of the injured have been identified. Of the 34 identified foreign nationals reported injured, none are Swedes, authorities say. Six of the injured have not been identified, and a further eight have not had their nationality identified.
The Swedish Ministry of Foreign Affairs does not yet have information about any affected Swedes.
Panic and chaos
Witnesses describe how New Year's celebrations suddenly descended into chaos and panic as people desperately tried to break windows to escape the flames. Others managed to escape the blaze.
Relatives are now desperately searching for missing friends and family members.
"I'm continuing to look for him; I won't give up," Laetitia Brodard-Sitre, whose 16-year-old son Arthur was at the bar, told BFM television.
An Instagram account shares photos of missing people. They are almost exclusively young people, some born as recently as 2011.
"We have tried to get hold of our friends. We have taken lots of pictures and put them on Instagram, Facebook, every social media outlet imaginable, to reach them," 17-year-old Eleonore told AFP.
"But there is nothing, no answer."
It is unclear how many people were at the bar. Swiss paper Blick reports that about 200 people were present when the fire started, and, according to AFP, the venue has a capacity of 300 people.
President Guy Parmelin has announced five days of national mourning.
