Giuseppe Conte, the prime minister, arrived in Genoa on Tuesday night and was expected to be joined later by his deputy, Luigi Di Maio.
Witnesses reported hearing a roar as the 45-meter (nearly 150-foot) bridge collapsed in a torrential rain during midday traffic on the eve of a major holiday that sees most Italians abandoning cities for beaches and mountains.
A large section of the Morandi viaduct upon which the A10 motorway runs collapsed in Genoa, Italy, on August 14, 2018.
More than 400 people were evacuated from 11 buildings located near or below the still-standing of the bridge, the city said.
"In the sad history of bridge collapses, maintenance has sometimes been a factor, if it is poorly planned or implemented", Mr Firth said.
Davide Capello, a former Cagliari goalkeeper, now firefighter, plummeted to the ground inside his auto when the bridge collapsed the Italian news agency ANSA reported.
Some 30 people were killed on Tuesday when a vast span collapsed during a heavy rainstorm, sending vehicles and their drivers plunging 100 metres onto railway tracks below. Video showed eyewitnesses screaming just after a section of the bridge gave way.
I saw traffic slow down, I heard a boom then people were running towards me.
The tender provided for a strengthening of the bridge's pier cables, including those of pier nine, the one that collapsed on Tuesday. "It was really an apocalyptic scene, I couldn't believe my eyes", he said.
But the head of the civil protection agency, Angelo Borrelli, said he was not aware that any maintenance work was being done on the bridge. So far, 16 people have been hospitalised, including 10 in critical condition, the agency said.
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Some 300 firefighters from across Italy have been using sniffer dogs and climbing gear in the search.
Rescuers are still working to pull out people from the rubble.
"It's not acceptable that such an important bridge. was not built to avoid this kind of collapse", Deputy Transport Minister Edoardo Rixi said on SkyNews24, speaking from Genoa. "We can't live with infrastructure built in the 1950s and 1960s".
Transportation Minister Danilo Toninelli called the collapse "an enormous tragedy", adding that if negligence played a role, "whoever made a mistake must pay".
A 2011 report by Italian highways company Autostrade per l'Italia said that the bridge had been suffering from degradation. "The bridge was constantly monitored and supervised well beyond what the law required".
"Operations are ongoing to extract people imprisoned below parts of the bridge and twisted metal", he said.
Autostrade said it would work with investigators to discover the cause of the disaster, and that it was already assessing how to rebuild the bridge.
That bridge "has also experienced problems during its life, so it could be that the design implies a need for a greater degree of maintenance than normal", Mr Firth said.
He told Sky TG24: "I was driving along the bridge, and at a certain point I saw the road in front of me collapse, and I went down with the auto". "But there will be a time when the cost of maintenance will be higher than a replacement", he told Italian media Primocanale.
Restructuring work on the bridge was carried out in 2016. The motorway is a major artery to the Italian Riviera and to France's southern coast.