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Rushing water filled the villa in Casteldaccia in the province of Palermo in moments, wiping out the families who were spending Saturday (local time) night there.
A father and his daughter escaped harm because they had left the house to do some shopping while a third person climbed a tree to survive.
The tragedy brings the number of people killed in Sicily this weekend to at least 12 after three other people died in their cars when hit by torrents of water.
Italian Prime Minister Giuseppe Conte spoke of "an immense tragedy" during a visit on Sunday to affected areas in Sicily.
He said a cabinet meeting would be convened this week to declare a state of emergency and come up with the first package of aid for areas affected.
Heavy rains and gale-force winds have battered Italy for several days, uprooting millions of trees and cutting off villages and roads.
Italy's Civil Protection Agency said deaths caused by the wave of bad weather stood at 17, excluding the fatalities in Sicily.
Some of the worst damage has been recorded in the northern regions of Trentino and Veneto.
On Saturday the governor of Veneto, Luca Zaia, said storm damage in the region amounted to at least a billion euros.
During a visit on Sunday to badly-hit areas in the north, Italy's Interior Minister Matteo Salvini said 250 million euros ($285 million) had already been earmarked for relief.
He said the government would be asking to use special EU funds.
Salvini, who is also deputy prime minister, said a rough estimate of how much it would cost to safeguard Italy against such events was 40 billion euros.