Search operations for possible survivors should resume on Monday the day after the tragedy.
On Sunday, at least six people died and eight others were injured after part of the Marmolada glacier, the largest in the Italian Alps, collapsed.
Relief spokeswoman Michela Canova told AFP on Sunday evening that the death toll, initially five dead, had risen to "six confirmed victims".
Eight injured are also to be deplored, she announced, without giving details on the nationality of the victims.
According to Italian media, foreign nationals were among the roped parties carried away by the avalanche.
The head of civil protection in the province of Veneto, Gianpaolo Bottacin, also mentioned "disappeared" on his Facebook account.
Alpine rescue has activated a toll-free number to allow reports to people who have not heard from relatives who have gone on an excursion on the glacier.
The head of the Italian government Mario Draghi sent in a message on Twitter "his most sincere condolences" to the victims and their families.
"The consequence of the current weather conditions"
Several helicopters were immediately deployed to take part in the rescue operations and monitor the evolution of the situation, but the search had to be suspended at nightfall before resuming on Monday morning.
This collapse occurred the day after a temperature record at the top of the glacier of 10°C.
The collapse of the Marmolada "is the consequence of the current meteorological conditions, that is to say an episode of early heat which coincides with the problem of global warming", explained to AFP Professor Massimo Frezzotti, from the department of Sciences from Rome 3 University.
“From what you can see in the footage, the collapse was significant.
We can see that there is a large quantity of water because the melting has accelerated in the Alps.
We had an extremely arid winter, with a rainfall deficit of 40-50%.
Current glacier conditions correspond to mid-August, not early July,” according to the researcher.
The rescue spokeswoman described "an avalanche of snow, ice and rock which in its path hit the access road when several roped parties were there, some of whom were swept away".
“The definitive number of climbers involved is not yet known,” she added.
The glacier collapsed near the locality of Punta Rocca, along the route normally taken to reach its summit.
The work of the rescuers, helped by canine units, was particularly difficult, because they had to extract the bodies from the gangue of ice mixed with rock where they were.