Rome has said Autostrade failed to ensure a safe structure and has begun a legal process with the aim of revoking concessions for Autostrade's entire Italian toll network, spanning nearly 3,000 km (2,000 miles).
Denise Vittone, sister of victim Andrea Cerulli who died with his wife and children, told La Stampa: "I no longer have trust in this state".
Families of other victims have opted for private funerals.
The death toll has risen to 42, according to media reports.
Anger is mounting over the tragedy and the structural problems that have dogged the decades-old Morandi bridge, which buckled without warning on Tuesday, sending about 35 cars and several trucks plunging 45 metres onto railway tracks below along with huge chunks of concrete.
Mr Stone added that members of the community have claimed they told Autostrade per L'Italia and the local government that the bridge was not safe.
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Civil protection department officials said Friday there might only be five people missing, but the exact number was fluctuating.
But rescuers have not given up hope of finding someone alive.
The cause of the unexpected tragedy is not yet clear.
Italy's government, however, started proceedings on Friday to begin stripping the toll bridge's operator, Autostrade, of concessions it holds to operate toll highways.
Autostrade has 15 days to respond to the letter.
Players and coaches of Genoa's two main soccer teams are among those attending the state funeral for victims of the city's bridge collapse.
"This disaster obliges us to take new initiatives which are much more rigorous than those adopted by previous governments", Prime Minister Giuseppe Conte said in a statement.
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Shares in its parent company Atlantia plummeted in the aftermath of the disaster. It said the bridge was monitored on a quarterly basis, as required by law, and extra checks were carried out by external experts.
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The study by engineers at Milan's Politecnico university was published in November 2017 and found that the stays of the section of the bridge that later collapsed reacted to vibration "in a way that does not entirely conform with expectations and requires further investigation".
One survivor, whose vehicle plunged from the bridge to the bottom along with falling sections of highway, told the Associated Press how as a trained firefighter he immediately understood that the structure had collapsed when the road dropped out from under him. He said had no major physical injuries.
The BBC's James Reynolds in Genoa says Italy's populist government is keen to show it is taking action.
The bridge collapse came after the country slashed its investments in infrastructure and cut its budget allocated to maintenance to bridges and streets. "The only road the government will follow is that of going forward with revocation procedures".
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