A fire service spokesperson told AFP that the bridge had mostly fallen on rail tracks 100 metres below and that cars and trucks had fallen with the rubble.
More than 400 people were evacuated from 11 buildings located near or below the still-standing of the bridge, the city said.
"People living in Genoa use this bridge twice a day", said Deputy Transport Minister Edoardo Rixi, who is from the city. "Obviously for me, it is not", said Deputy Prime Minister Matteo Salvini, head of the right-wing League, part of the ruling coalition.
Authorities said at least 30 cars and three heavy duty vehicles were on the 80-metre section of the bridge that collapsed.
Davide Capello, a soccer player, was on a motorway bridge in Genoa in Italy when it collapsed.
Asked about the collapse on a live broadcast, Mr Salvini responded: "We should ask ourselves whether respecting these (budget) limits is more important than the safety of Italian citizens".
It is not yet clear what caused the bridge to collapse, which came as maintenance work was being done on the bridge and as the Liguria region experienced torrential rainfall.
"There has not been sufficient maintenance and checks, and safety work for many bridges and viaducts and bridges in Italy constructed - nearly all - during the 1960s", he said.
After the collapse in Genoa, several people were pulled from the rubble alive, according to Italian media reports. It called for a "Marshall Plan" to fix or replace tens of thousands of bridges and viaducts built in the 1950s and 1960s.
Transportation Minister Danilo Toninelli called the collapse "an enormous tragedy", adding that if negligence played a role, "whoever made a mistake must pay".
Autostrade, a unit of infrastructure group Atlantia that is controlled by the Benetton family, manages the section of the toll highway that collapsed. The prosecutor's office in Genoa said it was ready to open a criminal inquiry.
Mr Brencich had already raised the alarm over the danger posed by the bridge in 2016, calling its span "a failure of engineering".
A former goalkeeper for Italian Serie A club Cagliari survived the deadly collapse of a motorway viaduct in Genoa on Tuesday despite going down with the bridge in his vehicle and finishing among the rubble.
A witness told Sky Italia television he saw "eight or nine " vehicles on the bridge when it collapsed in what he said was an "apocalyptic scene".
He did not say at the time that it was in danger of collapsing, but that it required continuous maintenance and would eventually have to be torn down and replaced.
The disaster occurred on a highway that connects Italy to France and other vacation resorts on the eve of a major Italian holiday on Wednesday, Ferragosto, and traffic would have been heavier than usual as many Italians travelled to beaches or mountains.
"This bridge has had quite a lot of maintenance work", said Ian Firth, past president of the UK-based Institution of Structural Engineers, and a structural engineer specialising in bridges.
As cranes moved in to shift truck-sized chunks of broken concrete, hundreds of firefighters searched for survivors, while public shock and grief turned to anger over the state of the 1.2 km-long bridge, completed in 1967 and overhauled two years ago.