A further six are missing, believed to be buried under the snow on the slopes of Mont Maudit – the third-highest peak in the massif, which is popular with climbers in the summer.
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France's deadliest avalanche in a decade occurred shortly after 5am local time, above the ski resort of Chamonix, at an altitude of 4,000 meters, and is reported to have hit two groups of roped climbers.
Mountain police said one of the survivors quickly raised the alert by telephone. Emergency workers with search dogs and helicopters mounted a rescue operation, and the injured were airlifted to hospital.
At least two Germans, two Swiss and two Spaniards, are among the dead, with Agence France Presse reporting that 28 people took part in the climb, from countries that also included France, Britain and Serbia.
An investigation has been launched to determine the cause of the avalanche, the French newspaper Liberation reported, after the mayor of Chamonix, Eric Fournier, said the local weather forecasts did not report an avalanche risk.
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According to France Info, the popularity of the route, used by dozens of climbers every day to access the summit of Mont Blanc, may have loosened the snow.
The prefect of the Haute-Savoie alpine region, Colonel Bertrand Francois, told journalists that it was possible one climber had triggered the avalanche, on the steep slope of the north face of Mont Maudit, sending down a 40cm-thick sheet of icy snow.
In a statement, the French Interior Ministry offered "its deep sympathy and full support" for those touched by the tragedy, adding that Interior Minister Manuel Valls would visit the scene this afternoon.