Rivers broke their banks at the height of the storm on Monday, sweeping away bridges, bringing down power lines and flooding hundreds of homes - some of them in low-lying rural areas that have yet to be reached.
"We are looking inside homes, inside basements, particularly in outlying areas," said Gianfranco Galaffu, local director of the civil protection agency for the worst affected northern part of the island.
"There is a lot to do. The activity is frenetic. For now we are taking care of the most acute emergencies," he said, adding that personnel and equipment were being sent in from other parts of Sardinia and mainland Italy.
Thousands were displaced by the flooding, said Environment Minister Andrea Orlando.
"Around 2,700 people had to leave their homes and are staying in community shelters or with their families," said Orlando, speaking in front of Italy's parliament.
The minister announced that an earlier death toll of 17 had risen to 18.
A government meeting on Tuesday declared a state of emergency for the island and allocated €20 million for emergency assistance, while the regional government provided five million euros.
A few people - estimated at between two and four by different officials - were still reported missing.
Rescuers said that more victims could be found in flooded homes or cars and that around 20,000 people had been affected.
Soldiers and navy personnel were deployed in the region, as local rescue services said their efforts were being hampered by the damage to roads. Rescue dogs were also being used, officials said.
"We are focusing on essential operations: saving human lives, assisting displaced people and clearing road access," Prime Minister Enrico Letta told a press conference after an emergency cabinet meeting.
'An absolutely extraordinary event'
"This was an absolutely extraordinary event," Letta said, with one expert saying that a storm of such intensity and with such high rainfall had not been seen on the picturesque holiday island "for centuries".
The port city of Olbia, a popular destination in the summer months, was swept by floodwaters which receded on Tuesday, and hotels, sports halls and private homes were being used to shelter displaced people.
Many local residents voiced anger saying they had not been warned sufficiently about the impending storm but the civil protection agency rejected the criticism, saying the area had been placed on red alert.
The victims included four children and an entire Brazilian family of four living in a basement.
Three people from another family were also killed 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 hospitalized suffering from hypothermia.
The heavy rain and high winds meanwhile shifted to the regions of Calabria and Campania in southern Italy and officials said they were monitoring the level of the River Tiber in Rome.
The holiday village of Sellia Marina in Calabria had to be evacuated, ferry services from Naples to the islands of Capri, Ischia and Procida were disrupted and St Mark's Square in Venice was under water.
Silvio Saffioti, head of the fire brigade for Sardinia, said that "many pump trucks" to remove floodwaters were themselves stuck in flooded areas.
Civil protection agency chief Franco Gabrielli said the island was "unprepared" for the flooding, caused by 440mm of rain in the past 24 hours alone - almost half the amount that usually falls on average in Italy over an entire year.
"I have found a lot of willingness, a bit less organisation," Gabrielli said after flying into Olbia, where he was overseeing rescue operations.
Experts blamed unregulated construction and poor maintenance of waterways for the flooding and said the problem was all over Italy, not just Sardinia.
"The area was not well managed," said Claudio Rafanelli, an expert on geological risks.
"You cannot build in flood plains and you have to keep the rivers clear. We are really behind on this."