Italy's civil protection chief, Franco Gabrielli, said one person remained unaccounted for and that the toll of 16 may still rise as crews reach isolated areas in the countryside where some homes are submerged.
The island, famed for its Costa Smeralda beaches of crystal clear water and dry Mediterranean climate, received more than 400 millimeters of water in 24 hours, he told Sky TG24.
Olbia Mayor Gianni Giovanelli said the city had been destroyed by the "apocalyptic" storm, with bridges felled by gushing, muddy rivers and water levels reaching 3 meters (10 feet) high in some places.
Premier Enrico Letta convened the cabinet Tuesday morning to declare a state of emergency to free up funding and resources.
Sardinia Gov. Ugo Cappellacci said among the dead was a family of four, reportedly of Brazilian origin.
Local newspaper L'Unione Sarda said one policeman helping to escort an ambulance died when the car he was travelling in was submerged in the collapse of a bridge in Dorgali. In hard-hit Gallura, three people died after their car was swept away in the collapse of another bridge, it said.
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