Authorities are still working on the formal identification of the 40 people killed in the fire, with police commander Frédéric Gisler saying “that is our priority”.
Many of those injured in the fire remain in a critical condition, authorities said.
Of those injured, 113 have been formally identified, Gisler said. This figure includes 71 Swiss citizens, 14 French, and 11 Italians, as well as four Serbs, among others.
The formal identification process of six others was ongoing, he said, and warned the figures may still change.
Among those injured were 19-year-old French footballer Tahirys Dos Santos, according to a statement released by his football club, FC Mertz.
Dos Santos was “severely burned” in the fire, the club said, and has been airlifted to Germany for treatment.
Mathias Reynard, president of the Valais region, said around 50 injured people “have been transferred or will be transferred soon to European countries in specialised centres for severe burns”.
“Many people were injured and are still fighting to live”, Mr Reynard said.
He added a ceremony will be held in Crans-Montana on 9 January so people can come together for a moment of “national mourning”.
Ms Pilloud later told the news conference the investigation would also explore whether the bar ceiling complied with building regulations.
She said investigators were exploring the installation of foam in the ceiling, adding she was unable to say with certainty at this stage whether the foam did or did not comply, or if it was installed with or without authorisation.
“It’s essential we don’t make any assumptions… leave us to do our work,” she said.
She said the two French managers of the bar had been interviewed, as well as people who escaped the fire.
Ms Pilloud said the interviews had helped them to establish a list of those who were present during the incident.
Lea Zehnder, 22, was celebrating New Year’s at a bar within eye-shot of Le Constellation.
She described hearing screams coming from Le Constellation and said her boyfriend helped those with serious burns.
“They couldn’t walk or talk”, she said.
Le Constellation is a large bar which has been around for many years.
It could hold up to 300 people and had a small terrace, although it is unknown how many people were there at the time of the fire.
On Friday, groups of tearful families and teenagers gathered near the police cordon around the bar.
Some left bunches of flowers and candles, while others placed messages at a makeshift shrine.
White tents covered the entrances and exits of the site.
Just outside town, a conference centre is being used to provide support to the families of the missing.