Authorities deployed a vast search mission, involving three helicopters, dozens of rescue workers, doctors, Alpine guides and sniffer dogs, said the statement.
The search for 10 missing climbers was suspended Sunday afternoon because of the risk that the warm weather could melt other ice blocks and provoke another snow slide, the statement and local police and government officials said.
The missing include five Austrians and three Swiss, and the nationalities of the other two were not immediately known, the statement said. Eight people were hospitalized.
Italy's ANSA news agency quoted unidentified French police as saying that only eight people were missing. Two Italians who were believed to be among the missing were not involved in the avalanche, and had already returned home safely, the report said.
Mont Blanc du Tacul is along one of the routes that mountain climbers often used to reach the summit of Mont Blanc, western Europe's biggest mountain at 15,780 feet.
The famed mountain straddles the French-Italian border draws thousands of visitors each year, and the area is known for hiking, skiing and mountaineering.
Mont Blanc du Tacul is usually scaled by seasoned climbers, who either want to reach its summit or carry on to the Mont Blanc peak.
In summertime, they often climb through the night because cold temperatures keep the snow and ice hard, reducing the chance of sinking - and lowering the avalanche risk.
Climbing to the Mont Blanc du Tacul peak can be done in a day, while proceeding to the Mont Blanc summit would generally add at least another day of climbing.
Avalanches intermittently hit the celebrated Mont Blanc range, where dozens of climbers die every year.
Two French climbers in a Swiss sports club died in an avalanche on Mont Blanc in August 2006. In another in July 2005, a British soldier was killed while taking part in an altitude training course on Mont Blanc du Tacul.