At least four people were pulled alive from vehicles under the bridge, ANSA reported.
A huge section of the Morandi Bridge fell at midday over an industrial zone, sending tons of twisted steel and concrete onto warehouses below.
In its latest update, the government of the Liguria region tweeted that 19 bodies had already been identified and 15 people had been admitted to hospital, nine in critical condition.
One unidentified man, who had been standing beneath the bridge at the time, was thrown more than 30 feet and into a wall when it collapsed.
One eyewitness, who gave his name as Andrea Rescigno and said he was in his auto at the time of the bridge collapse, said in a phone interview with Genoa TV station Primocanale that he saw "cars and trucks plunging into the void".
Firefighters still heard voices from under the rubble up until an hour ago, fire official Bruno Frattasi told state broadcaster RAI, saying that seven survivors had been pulled out so far. "We need to remove all of the rubble to ascertain that all of the people have been reached", he said.
What caused the Morandi Bridge to fall remained unknown, and prosecutors said they were opening an investigation but had not identified any targets.
"We should ask ourselves whether respecting these (budget) limits is more important than the safety of Italian citizens".
The government has pledged to increase public investments and lobby the European Commission to have the extra spending excluded from E.U. deficit calculations.
Salvini also said he wanted the "names and surnames of those who are to blame, because a tragedy like this in 2018 is not acceptable".
She said it's lucky it's summer, which means less people would be using the bridge as they're on holiday. One truck was shown just metres away from the broken end of what locals call the "Brooklyn Bridge".
"Suddenly the bridge came down with everything it was carrying".
Authorities said at least 30 cars and three heavy duty vehicles were on the 80-metre section of the bridge that collapsed.
Around 200 firefighters and sniffer dogs searched for survivors among the wreckage.
It was unclear what had caused the collapse, but the event raised questions among some Italian government officials about maintenance of their country's infrastructure - a common concern in developed countries, where numerous major roadways were built decades ago.
Transport Minister Danilo Toninelli told Italian state television the disaster showed the dilapidated state of Italy's infrastructure and a lack of maintenance, adding that "those responsible will have to pay". The collapsed section was 50m high.
He said: "The collapse was unexpected and unpredictable. There was no reason to consider the bridge unsafe".
Autostrade said it would work with investigators, and that it was already assessing how to rebuild the bridge.
Borrelli said highway engineers were checking other parts of the bridge and that some areas were being evacuated as a precaution.
The bridge was inaugurated in 1967 and is about 0.6 miles long.
The company that operates and maintains the highway, along with many other roads in Italy, said in a statement Tuesday that "stabilization" work was ongoing at time of the collapse.