"Twelve dead in Sicily, people lunched by water," Interior Minister Mateco Salvini said in a statement to the press in the north of the Veneto.
Nine of the people were members of two families who were eating together when the house was submerged by water from a nearby river that suddenly overflows, said the Fire Brigade on Twitter.
The Fire Brigade said on Twitter that its divers found the bodies. Among the victims were two children aged 1 and 3 years old.
The Civil Protection Agency said it was still looking for a doctor who was in his hospital workshop on Saturday night and is now missing.
Strong winds and intense rains have destroyed parts of the country last week, causing the worst floods in at least a decade in Venice, more than 1 billion euros in Veneto and landslides that have interrupted villages, authorities said.
The situation in Sicily is "dramatic," Prime Minister Giuseppe Conte said on Sunday.
Mr Conte will call a cabinet meeting to announce a state of emergency in the affected areas, he said at a press conference in Palermo, Sicily.
Italy's Civil Protection Service continues to monitor the situation by issuing weather warnings via Twitter, while Italian Red Cross volunteers are working to rescue people.
Several of last week's deaths were caused by the fall of the trees as strong winds of 190 kilometers per hour (118 miles per hour), with the damaged forest acres, including the famous "Violin Forest" that provided the wood for violin instruments Antonio Stradivarius .
Two young people died south of Rome when a tree hit their car. Another was hit by a fall tree while walking in Naples.
About 300,000 trees were flattened after the winds swept the Val d 'Assa on the Asiago plateau, Roberto Ciambetti, president of the Veneto Regional Council, told CNN.
"Tens of thousands of tall trees were taken up like toothpicks," he said.
Much of Venice was under water, as strong winds on Monday led the tide to one of the highest levels ever recorded.
St. Mark's Square became a lake and the waters were flooded on the ancient marble floors of St. Mark's Basilica.
"In one day, the 20-year-old basil, but perhaps an optimistic view," Carlo Alberto Tesserin, head of the St. Mark's Basil's Board, said in a statement.
Floodwaters also covered several dozen square meters of 1,000-year-old marble pavement in front of the change of Madonna Nicopeia, a 12th-century picture, and sank into the Baptistery and Zen Castle, Tesserin said.
Flood barrier program incomplete
This week's floods were caused by a seasonal flow and a strong low-pressure system in southern Europe that brought strong winds from the south and pushed the water into the Adriatic Sea in Venice. This is the peak season of the year for the seasonal floods known as acqua alta, or with water, in the city.
The floods in the tide have become much more common in Venice due to climate change – a problem that will continue to deteriorate as seas rise due to rising temperatures and melting ice sheets, according to CNN meteorologists.
Work on installing innovative underwater flood dams to protect Venice from serious flooding, known as the Moses project, has begun for years. However, it has not yet been completed, partly because of corruption and rising costs.
A representative of the Civil Protection Agency in Venice told CNN that the Moses system could mitigate the effects of seawater on historical sights of the city.
"Of course, if the work of Moses was completed, the damage we see now would not have happened," he said, "but the project was not completed due to the high cost."
The representative of the mayor's office asked for the completion of the project.
"The work of Moses is important to the Venetians," he said. "This infrastructure must be completed to avoid extraordinary waters, as happened on Monday."
A spokesman for the New Venice Consortium, who is in charge of the Moses system, told CNN: "Work on Moses began in 2003. At this time 92-93% is over."
Venice also has a tidal monitoring and warning system for high water levels.