The death toll rose on Wednesday morning in what the Italian government has called an "immense tragedy".
The cause of the disaster was not immediately clear, although the national motorways body said on its website that it had been conducting maintenance works on the base of the viaduct.
Speaking from the site of the collapse, Italy's Prime Minister Giuseppe Conte said "all infrastructure" across the country needs to be double-checked.
Aerial footage showed more than 200 metres of the viaduct, known locally as the Morandi bridge, completely destroyed.
Helicopters were used to lift dozens of survivors on stretchers from the ruined bridge.
A very careful investigation will have to be carried out into how the bridge, which was finished in 1967, collapsed so suddenly, RFI Rome correspondent Sabina Castelfranco says. Questions have been raised about the maintenance and whether it was carried out correctly or not.
Early speculation that a lightning strike could have triggered the collapse has been rejected by authorities, she said, although there remains doubt as to what role weather played in the accident as the collapse happened during a particularly bad thunderstorm after weeks of extreme heat.
Italian President Sergio Mattarella said a "catastrophe" had hit Genoa and the whole of Italy.
"Italians have the right to modern and efficient infrastructure that accompanies them safely through their everyday lives," Mattarella said in a statement.
Interior Minister Matteo Salvini who is also leader of the far-right League party in the coalition government, vowed to hold those responsible for the disaster accountable.
"I have gone over this bridge hundreds of times and I commit to digging and finding out who is responsible for an unacceptable tragedy, because it's not possible that in 2018 you can work and die in these conditions," he said.
French President Emmanuel Macron reacted quickly to the disaster, taking to social media to express his condoleances in French and Italian and offer any necessary assistance.