Another said rescuers are trying to dig out the five missing using shovels as mechanical diggers cannot reach the area.
It is unclear if they are still alive, the official added.
According to France Info, the group was made up of eight holidaymakers led by a guide. As reported by the rescue teams, some of the victims are believed to be younger than 20.
The identities and nationalities of those killed have not been announced.
He said two of the four people killed had died shortly after emergency workers pulled them out alive, and a total of nine people were hit by the avalanche.
The avalanche was apparently triggered by skiers higher up the slopes, the resort said in a statement.
Two helicopters, rescue teams and sniffer dogs are searching for the missing.
The avalanche risk in the area on Monday was listed as 3 on a scale of 5.
The 400-metre wide avalanche occurred at an altitude of 2,100 metres in an off-piste section of the ski area at Tignes, a popular resort near the Italian border.
Police and emergency services were rushed to Tignes from the nearby resort of Courchevel to reinforce those already at the scene.
It was a so-called "slab" avalanche, caused when dense, wind-packed snow breaks off, the ski resort said.
Avalanches can travel at up to 400km per hour.
One of the worst avalanches in the past 10 years took place in the Mont-Blanc range in the summer of 2012. Nine climbers from Britain, Germany, Spain and Switzerland were killed as they tried to scale the north face of Mont Maudit.
Last month, 29 people died in Italy after an avalanche buried a hotel in the central town of Rigopiano.
- Originally published in Telegraph UK
