Four people from the same family were found dead in a flooded house in the city, where 40 centimetres of rainfall in four hours transformed streets into rivers and washed away cars.
The Corriere della Sera daily said the dead were a little boy, her parents and a grandparent, all found in a basement apartment, local daily Il Tirreno said.
The grandfather, who lived on first floor, had managed to rescue a three-year-old girl from the basement but died when he went back to try and save a four-year-old boy, it said.
A fifth body was found in an area devastated by landslides, while a sixth was found in a nearby hilltop neighbourhood. A seventh person was killed in a road accident, though it was not yet clear whether it was due to the weather. Two other people were still believed to be missing, the fire brigade said.
"The situation is very difficult, it's critical. We fear a disaster," Livorno mayor Filippo Nogarin said.
He said the government had underestimated the danger, issuing a code orange alert for the region rather than red.
"We didn't expect this because the alert was orange. Then we woke up to this," he said adding that the death toll "may still rise" and could have been avoided entirely if they had known what was coming.
Italy's civil protection service issued a code orange alert for Florence as the storms, which began in northern Italy overnight, swept down the country towards the south.
Underpasses were being closed as a precaution in the capital Rome.
"What's happening in Rome right now is unheard of... with a storm unleashing chaos. Once more the city has proved itself to be completely unprepared for rain," said Italian consumer association Codacons.
Coldiretti, Italy's main agricultural organisation, said the bad weather was aggravated by coming hard on the heels of a drought which had left the land drier than usual and unable to soak up the rains. Rainfall in Tuscany in particular had been down 57 percent this summer, it said.
"The tropicalisation of the climate is causing an increase in extreme weather events, with heat waves, heavy cloud bursts and violent hailstorms which are damaging the national agricultural production," Coldiretti said.
It put the cost of the damage at over €14 billion in the last 10 years.