Rescuers have little hope of finding more survivors underneath the Morandi bridge, where almost 40 vehicles fell 45m (148ft) in Tuesday's collapse.
The cause is not yet known but there have been calls for the heads of the company operating the bridge to resign.
Survivors have also been recalling the horror of the bridge's collapse.
Hundreds of firefighters worked overnight with lifting gear, climbing equipment and sniffer dogs to try to locate more survivors. But an Italian Red Cross spokeswoman told the BBC's Tim Willcox that only bodies had been found.
The local prefecture raised the death toll on Wednesday morning to 39, 37 of them identified. At least three children lost their lives.
The city's authorities have declared two days of mourning.
There are 16 people being treated in hospital, 12 of them in a serious condition.
Some 440 people were evacuated from the area. Residents of council housing blocks under one pillar were ready to move back, but were then told it was cracking and their homes were at risk.
The Morandi bridge, built in the 1960s, stands on the A10 toll motorway, an important conduit for goods traffic from local ports, which also serves the Italian Riviera and southeast coast of France.