"There has not been sufficient maintenance and checks, and safety work for many bridges and viaducts and bridges in Italy constructed - nearly all - during the 1960s", he said.
Some 200 firefighters were on the scene, the fire service said, and Sky Italia television said four people had been pulled from the rubble. Authorities said at least 20 people were killed, although the death toll fluctuated throughout the day and some people were found alive in the debris.
Mr. Salvini also said he wanted the "names and surnames of those to blame because a tragedy like this in 2018 is not acceptable".
Prosecutors said they were opening an investigation but had not identified any targets.
State radio reported Wednesday that some 5-Star lawmakers in 2013 had questioned the wisdom of an ambitious and expensive infrastructure overhaul program as possibly wasteful, but that a post about that on the Movement's site was removed on Tuesday after the bridge's collapse.
The bridge sees some 25 million vehicles every year, and a 2011 report by an Italian highways company said that the bridge had been suffering from degradation.
Poorly carried out maintenance can sometimes be a factor in a bridge collapse.
The head of Italy's civil protection agency, Angelo Borrelli, said 30-35 cars and three heavy trucks were on the 80-meter (260-foot) section of the bridge that collapsed.
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The ANSA news agency reported Mr Capello called his father while he was stuck in his auto and told him he was safe and not to worry.
Danilo Toninelli, the transport minister, said on Wednesday that the top level of Autostrade per l'Italia "must step down first of all".
Ponte Morandi, built in the 1960s, was undergoing repairs when the tragedy happened.
Autostrade, a unit of the infrastructure group Atlantia, controlled by the Benetton family, manages the section of the toll highway that collapsed. "The bridge was constantly monitored and supervised well beyond what the law required", Stefano Marigliani, the Autostrade official responsible for the Genoa area, told Reuters.
He said there was "no reason to consider the bridge was unsafe". "We're going to work round the clock until the last victim is secured".
The design of the elevated road had been criticised in the past. The break sent huge slabs of concrete plummeting into two warehouses, some railroad tracks and a riverbed below the bridge. "But there will be a time when the cost of maintenance will be higher than a replacement", he told Italian media Primocanale. But he added that they were about to launch a 20 million euro ($22.7 million) bidding process for significant safety work on the bridge.
The disaster occurred on a major artery to the Italian Riviera and to France's southern coast.
Autostrade said it would work with investigators, and that it was already assessing how to rebuild the bridge.
The government has pledged to increase public investments and lobby the European Commission to have the extra spending excluded from E.U. deficit calculations.