Pope Francis said he was praying for the victims and their families.
"The tragedies that we are experiencing with climate change should force us urgently to pursue new ways that respect people and nature," he said on Twitter.
Four victims were identified on Monday, three of them Italian, including two alpine guides, and another from the Czech Republic, news agency AGI reported, citing rescuers.
Rising average temperatures have caused the Marmolada glacier, like many others around the world, to shrink steadily over recent decades.
"The Marmolada glacier collapse is a natural disaster linked directly to climate change," said Poul Christoffersen, a professor in Glaciology at the University of Cambridge.
"High elevation glaciers such as the Marmolada are often steep and relying on cold temperatures below zero degrees Celsius to keep them stable," he said.
"Catastrophic glacier collapses such as this are becoming more frequent."
Luca Biagini, a former head of alpine guides said the disaster was, however, "unpredictable, nothing could have led us to expect something like this".
He added that the high temperatures were an important factor but there had been hotter seasons in the past, including a record-breaking summer in 2003.
Italian Prime Minister Mario Draghi and the head of the National Civil Protection agency were due to visit the area later on Monday.
