A major rescue operation was launched following the disaster on Mont Maudit, in the Mont Blanc range, near Chamonix. Mont Maudit translates as Cursed Mountain.
The Prefecture de la Haute-Savoie said that three Britons, two Spaniards, three Germans and one Swiss person also died while four people, whose nationalities are not known, are missing.
The Foreign Office said that five Britons were missing but could not confirm the British deaths or whether they were among the five.
Several dozen gendarmes and other rescuers along with two helicopters worked to pull the dead and injured from the mountain after the alarm was raised at 5.25am.
French Interior Minister Manuel Valls visited the area and flew over the avalanche site.
Speaking at a press conference afterwards, he said: "We are still searching for those who have disappeared.
"My thoughts are with those victims, with the British and Spanish and German victims, Swiss victims, and my thoughts are with their families who have discovered this painful tragedy. It is a personal one.
"Regarding the circumstances of this avalanche, as you know the investigation is under way and the prosecutor general is looking into this.
"We have seen many accidents on the Mont Blanc mountain but we should note that the number of victims and those who have disappeared and the injured is very high.
"This accident is catastrophic."
A spokeswoman for the prefecture said the local gendarmerie were alerted at 5.25am that two groups of climbers were in trouble on the northern face of Mont Maudit at 4,000m.
She said that at 5.45am the emergency services were told it was a "slab" avalanche which had hit several groups of mountaineers who were roped together.
Some of those caught in the avalanche were supervised by professional mountaineering guides but others were climbing independently.
The spokeswoman said nine people were taken to hospital in Sallanches with minor injuries and a chapel had been established in the hospital in Chamonix to help families involved in the tragedy.
A total of 28 people left a climbing hut to attempt the route.
The spokeswoman said some had crossed the path of the avalanche before it hit and others were able to turn back.
A Foreign Office spokesman said: "We are aware of the avalanche in the French Alps near Chamonix today and reports three British nationals have died.
"We are urgently seeking information from the rescue authorities, but as yet do not have official confirmation of these deaths.
"We are aware of five missing British nationals and are urgently working to establish their whereabouts.
"Consular staff from the British Embassy in Paris are en route to the area to offer consular assistance."
The FCO has set up a phone number for concerned relatives and friends to contact. It is 0207 008 1500.
British climbers have expressed their concerns and condolences.
A message on the British Mountaineering Council website said: "We hope the missing climbers are located soon, send condolences to the family and friends of those killed and wish a speedy recovery to those injured."
Chamonix-based mountain guide Richard Mansfield said the route where the accident happened was the second most popular to the top of Mont Blanc.
He said: "It's a very beautiful area and a common route, but it can have very serious consequences, particularly due to avalanches."
British mountaineer Kenton Cool said: "First and foremost, I'm absolutely shocked and saddened. My thoughts go out to the families."
Mr Cool, who lived in Chamonix for many years and still has a house in the area, said: "That area is quite notorious for this kind of thing."
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