Several people were still reported missing and emergency workers were trying to access low-lying rural areas affected by the heavy rain and high winds on Monday, which saw many rivers break their banks.
"We have decided to call a cabinet meeting to declare a state of emergency that will help boost rescue operations and allocate resources. The priority is to save human lives," Prime Minister Enrico Letta said.
"This is an incredible tragedy," Letta said.
The port city of Olbia, a popular holiday destination in the summer months, was left almost entirely under water and hotels, sports halls and private residents on the island put up people displaced by the flood.
"The number of victims has risen to 17 and several people are missing," regional governor Ugo Cappellacci said on news channel SkyTG24.
"The operation to provide basic necessities to the evacuees is under way. We are planning to restore electricity, start pumping out water from flooded areas and clear the roads," Cappellacci said.
Gianfranco Galaffu, a local director of the civil protection agency, told AFP that "around 20,000 people" had been affected by the flooding in Sardinia.
"We are still trying to reach some parts of the lowlands. There could be more victims in their cars... But the worst of the emergency is over," he said.
Among the dead was an entire family of four Brazilians who drowned in their basement flat in the town of Arzachena in the northern part of the island.
Three people from the same family also died when a road bridge collapsed onto their van near Olbia, while a mother and daughter were found dead in a car that was swept away in the city by surging waters.
A 64-year-old woman died in her flooded home in Uras in the southwestern part of the island, while her husband was hospitalised suffering from hypothermia.
Rescue efforts were concentrated in a mountainous region near Nuoro, where many people climbed onto the roofs of their homes or up trees to escape the
Civil protection agency chief Franco Gabrielli said the island was "unprepared" for the flooding and many local residents took to social media to complain that they did not receive sufficient warning about the forecast.
Gabrielli said that there had been 440mm (17.3 inches) of rain on the island in the past 24 hours - many times more than usual at this time of year.
"We are only just starting the rescue effort. I have found a lot of willingness, a bit less organisation," Gabrielli was quoted by Italian media as saying after flying into Olbia to oversee the rescue operations.
"The extent of the areas that still have to be reached is significant. Our aim is to reach as many people as possible as quickly as possible," he said.