The Morandi Bridge, named after the engineer who designed it, forms part of the A10 motorway run by Autostrade.
Firemen worked through the night looking for any survivors buried under the rubble.
Fire brigade spokesperson Luca Cari said 400 firefighters were at the site, lifting big chunks of concrete to create spaces for rescue teams to check for survivors.
The head of Italy's civil protection agency, Angelo Borrelli, said 30-35 cars and three heavy trucks were on the 80-meter (260-foot) section of the bridge that collapsed.
Images from the scene show a huge section of the bridge missing, with vehicles perched close to the edge.
Zoppi warns that it is impossible that similar tragedies won't happen again without serious work on infrastructure built post-World War II. I do not know when. Rescuers had hoped that their child had survived but when they retrieved the body it was limp.
"There are buildings that have been hit but it seems that all the victims were on the bridge".
"We have a duty to plan an extraordinary measure to monitor the state of infrastructure across the country", Conte told reporters in Genoa on Tuesday.
"The collapse could have been influenced by the consequences of increases in heavy traffic and the punishing treatment the motorway got".
Autostrade, a unit of the infrastructure group Atlantia, controlled by the Benetton family, manages the section of the toll highway that collapsed.
It is not yet clear what caused the disaster, but several explanations have been offered.
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The highway connecting France and the Italian Riviera is popular with tourists.
"Many of the bridges of the developed nations are at the end of their design lives", he said.
"There will be a time when maintenance costs will exceed those of reconstruction, and then we will have to proceed with the replacement".
In the 1990s, some major repairs were done to the bridge.
Matteo Pierami drove across the bridge with his wife and child, aged two months, nearly an hour before it collapsed.
Anil Agrawal, Professor of Civil Engineering at the City College of NY told CNN that if there is corrosion in the concrete, water can cause a void, further corroding the cables.
"They will have to pay, pay for everything, and pay a lot", he said. Antonio Brencich, a professor specializing in reinforced concrete construction at the University of Genoa, called the span "a failure of engineering" in an interview in 2016.
"And given that there have been breaches (of contract), I announce that we have begun the process for the eventual revocation of their contract and a fine of 150 million euros ($170 million)", transport minister Danilo Toninelli said on Facebook.
Officials said no warehouse personnel were inside, since it was closed for summer holidays. He told RAI television the government meant to cancel its deal to manage the A10 toll motorway connecting Genoa to French border.
Authorities are also advising residents to avoid the highways and to just use local roads for their daily activities.