Rescue efforts to find four other climbers still missing were called off until Friday and French Interior Minister Manuel Valls said an investigation would be launched to establish what had happened and how similar avalanches could be avoided.
The dead included three Britons, three Germans, two Spaniards and one Swiss, authorities said. The missing climbers are two Britons and two Germans. Nine people were injured.
A preliminary investigation suggested a climber may have stepped on an icy patch, unwittingly triggering the giant slide. Many of the climbers were roped together for safety reasons, and some of the injured sustained broken bones.
"The conditions are still perilous. At this stage, the mountain is not safe," Valls told reporters, adding that he had flown over the area and saw giant blocks of ice beneath him.
"Unfortunately, it's always in July and August that we get such events, but we will investigate and see if there is anything we can do."
Deadliest Since 2008
The most deadly avalanche in the Alps since 2008 swept down a popular climbing route in the Mont Blanc range near the border with Switzerland at about 0300 GMT. The scene of the tragedy - "le Mont Maudit" which translates as "Cursed Peak" - is one of two popular access routes to the famous Mont Blanc peak.
About 38 climbers were on the mountain - at an elevation of 4,000 metres (13,000 feet) - when the avalanche hit without warning in fine weather conditions, the head of the Haute-Savoie rescue squad, Bertrand Francois, told a news conference.
That included 28 climbers in two separate climbing teams, as well as solitary climbers, he said, adding that some of the climbers had managed to turn and flee.
Authorities had not expected any avalanches, as conditions were good on Thursday morning, said Jean-Louis Verdier, mayor of the resort town of Chamonix.
"We had no more reason than usual to be alarmed," Verdier told Reuters TV. "It's a steep mountain face. There are big plates of snow we know of where an avalanche can easily occur. But this morning we had no reason to expect an avalanche of this size and such a tragedy."
One of the climbers who managed to escape alerted the authorities.
Rescue workers in helicopters and on foot, as well as dog teams, had searched for the missing, but their efforts were hampered by the risk of a fresh avalanche as well as by high winds.
The search was called off on Thursday evening and will resume on Friday if the weather is good enough, French TV reported, quoting police.
Victims' families were being received at a chapel of rest set up at the hospital in Chamonix.
Eight Swiss, German and Austrian climbers perished in a similar avalanche nearby in 2008.
(Additional reporting by Catherine Lagrange; Writing by Alexandria Sage and Andrew Osborn; Editing by Diana Abdallah)