By Dave Graham and Emma Farge

CRANS-MONTANA, Switzerland, Jan 3 (Reuters) - Two people who ran a Swiss bar that burst into flames during a New Year's Eve party, killing 40, are under criminal investigation on suspicion of offences including homicide by negligence, prosecutors said on Saturday.

Two days after the fire, in which 119 people suffered injuries including severe burns, officials were still trying to identify many of those killed and attention turned to how one of Switzerland's worst tragedies could have occurred.

The bar's two operators are suspected of offences including homicide by negligence, causing bodily harm by negligence and arson by negligence, prosecutors in Valais, the canton that is home to the bar in the upscale ski resort of Crans-Montana, said in a statement. They did not name the pair.

"It was an enormous tragedy. We're all so sorry that this had to happen," Swiss Justice Minister Beat Jans told reporters, standing in front of the cordoned-off bar, Le Constellation.

He said temperatures during the blaze must have reached "500, 600 degrees (Celsius, 900-1,100 Fahrenheit)".

Reuters was not immediately able to contact the bar's owners for comment or reach the prosecutors to verify whether they were the people referred to.

Responding to the news of the criminal probe, residents still grieving over the sudden loss of life said it was important authorities get to the bottom of the case.

"We need a moment to reflect," said one, Patricia Mazzoni, 55. "But afterwards, I'd like an independent investigation. An independent investigation to find out who failed here."

Witnesses reported seeing staff at Le Constellation carrying so-called fountain candles atop bottles of champagne, and questions have also arisen about a foam material used to soundproof the ceiling of the basement where revellers danced.

Beatrice Pilloud, chief prosecutor of Valais, said indications were that the fire started because the sparklers got too near to the ceiling.

"From there, a rapid, very rapid and widespread blaze ensued," she said on Friday afternoon.

Investigations will look at renovations made to the bar, the fire extinguishing systems and escape routes, as well as the number of people inside when the blaze began, prosecutors said.

Police arrived quickly at the scene, according to local residents, but the fire burned victims so severely that investigators said they would need days to identify the bodies. 

Illustrating the painstaking nature of that work, the Valais prosecutors' office said on Saturday that the police had identified the bodies of four Swiss victims aged between 16 and 21 - two female and two male - and returned them to their families. It did not name them.

On Friday, officials had only identified one of the dead, a teenage Italian international golfer, Emanuele Galeppini. 

According to two people familiar with the investigation, some of the victims may be under 16.

Local residents said the bar was popular with young people and the Swiss government said many of the dead were likely youths. Beer and wine can be drunk from age 16 in Switzerland.

One of the bar's two owners, Jacques Moretti, told the Tribune de Geneve newspaper that Le Constellation had been checked three times in 10 years and that everything was done according to the rules. 

Stephane Ganzer, head of security in Valais, said the investigation would determine if the bar had undergone its annual building inspections, but that the town had not raised concerns or reported defects to the canton.

(Reporting by Dave Graham, Emma Farge, Tassilo Hummel and Benoit Van Overstraeten, Francois Murphy and Horaci GarciaEditing by Lisa Shumaker and Susan Fenton, Kirsten Donovan)