The death toll is expected to rise after a vast span of the Morandi Bridge in the north-western port city crumbled on Tuesday, sending around 35 cars and several trucks on a deadly plunge onto the railway tracks below.
The victims include children aged eight, 12 and 13, Interior Minister Matteo Salvini said on Wednesday.
The new coalition government has blamed Autostrade per l'Italia, a private sector company owned by Atlantia, for the tragedy.
"The first thing that should happen is that the heads of Autostrade per l'Italia should step down. 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.
Far-right leader Salvini, who is also co-deputy prime minister, said he was in "absolute agreement" with Toninelli.
Fellow deputy premier Luigi Di Maio, who is expected in Genoa by 1100 (0900 GMT), said the tragedy "could have been avoided", adding that those responsible for the disaster had a "name and surname".
"For years we have told ourselves that allowing private sector to manage (public assets) would be better than leaving it to the state," Di Maio, who heads the anti-establishment Five Star Movement, told Radio Radicale on Wednesday.
"Today we have one of the largest concessionaires in Europe telling us that there wasn't anything that could have led them to believe that the bridge could collapse. Autostrade should have done maintenance and didn't do it."