At least seven people were killed in the avalanche on Sunday on the Marmolada, which at more than 3,300 metres (10,830 ft) is the highest peak in the Dolomites, a range in the eastern Italian Alps straddling the regions of Trento and Veneto.
"When we arrived we saw a disaster, we realised the dimensions of this enormous avalanche," said Stefano Coter, head of the local alpine rescue team and one of the first people to reach the scene.
"We found injured people in need of help and other people who were dead," he added.
Much of Italy has been baking in an early-summer heatwave and scientists said climate change was making previously stable glaciers more difficult to predict.
With the peak still unstable, rescuers have been using drones and helicopters to look for victims or try to locate them through their mobile phone signals. The teams found human remains or climbing gear at three or four sites on Tuesday.
There had been fears that the death toll could go much higher, with a further 13 people still unaccounted for on Tuesday morning, but that figure came down to five missing people over the course of the day.
Seven people on the missing list have now been located, ANSA news agency reported. An Italian who was also unaccounted for had in fact been having treatment for his injuries in a hospital in the town of Treviso, near Venice, since the accident on Sunday.
The Marmolada will remain closed to tourists for the time being to allow rescue teams to operate, said Giovanni Bernard, the mayor in the local town of Canazei.
Hikers in the area said they were in any case frightened and would try to stick to safer routes.
"Right now after what happened I feel a bit scared because two days ago we were about to walk just near the glacier. It could have happened to us," said Mikael Bouchard, a 29-year-old from Lyon.
(Writing by Keith Weir; Editing by Mark Heinrich)
By Guglielmo Mangiapane and Roberto Mignucci