Liguria's president Giovanni Toti said in a news conference that one auto was reportedly involved but that he had no evidence and searches were continuing. It was not known iwhether any vehicles might have plunged off the highway, which is supported by pillars at that point.
But pictures of the damage brought back memories of the 2018 collapse of the Morandi bridge at Genoa, only 50 kilometres (30 miles) away, which claimed 43 lives.
On Sunday, it was not known if any vehicles had plunged off the road along a viaduct about a mile outside Savona, linking it to Turin.
And in northern Italy, a woman was found dead after the Bomida river swept away her auto. Images on French media showed cars peeking above inundated streets and waves slamming onto roadsides.
The administration for France's Var region said four people died, including a couple in their 70s from the perfume capital of Grasse whose vehicle got submerged.
The second body, of a man in his 50s, was found in the village of Cabasse in a auto, the local authorities said, without giving further details.
There were rain-swollen rivers and flooded streets throughout Italy, where there has been heavy rainfall in much of the country for the past two weeks.
In Turin, the Po river spilled over and flooded the medieval quarter as well as a popular riverside walking area.
Emergency crews on Sunday recovered the bodies of two people missing after storms lashed south-eastern France.
The worst hit region in Italy was Alessandria, south of Turin, where 200 people were evacuated and 600 left isolated. The region struggled with mudslides that blocked several roads, isolating hamlets.
Venice was partially flooded, but the high tide's level of almost 1.3 metres (4.3 feet) in late morning was not unusual for the lagoon city accustomed to the phenomenon of "acqua alta", (high water).
That level was almost two feet lower than the exceptionally high wind-driven tide that devastated the art-rich tourist destination earlier this month.
Venice's mayor has said the damage of the flooding earlier in the month could amount to one million euros, blaming the near-record water level rise on climate change.
In the Apulian city of Lecce, authorities ordered parks and cemeteries closed for fear that storm-battered trees might crash on to visitors, Italian news agency ANSA reported. Local media reported that two other people in the auto had managed to escape in time.
In France, rivers started receding slowly nonetheless many households who evacuated peaceable couldn't return dwelling.
French interior minister Christophe Castaner said more than 1,600 people have been evacuated.