The service, which coincides with a national day of mourning, came as firefighters still searching for five missing people discovered a car with human remains inside.
Local media reported a family of three had been discovered, including a nine-year-old girl, adding to the death toll of 38.
The populist government has blamed the operator of the viaduct for the collapse and threatened to strip the firm of its contracts.
Thousands of mourners flocked to bid farewell to the victims whose coffins, adorned with flowers and photographs, lined an exhibition hall turned into a makeshift chapel, Presstv reported.
"I lost a friend but I came for all the victims," Nunzio Angone told AFP.
Among the coffins was a small white one for the youngest victim, an eight-year-old boy who was killed alongside his parents.
Another two were draped in the Albanian flag featuring a black eagle against a red background.
Applause erupted as firefighters entered the hall ahead of the ceremony, which began at 11:30 am (0930 GMT), according to an AFP reporter.
But more than half of the families of the victims refused to take part, some preferring a more intimate funeral, while others announced a boycott.
"It is the state who has provoked this; let them not show their faces, the parade of politicians is shameful," the press cited the mother of one of four young Italians from Naples who died.
Roberto, father of another of the dead from Naples used social media to vent his anger: "My son will not become a number in the catalogue of deaths caused by Italian failures."
"We do not want a farce of a funeral but a ceremony at home."
Archbishop Angelo Bagnasco, who is expected to lead the mass, expressed his respect for those who refused state funerals.
Italian President Sergio Mattarella and Prime Minister Giuseppe Conte are due to preside over the state funeral, which local media say will also be attended by senior staff of infrastructure giant Autostrade per L'Italia, the managing company of the highway.
Mourners also included the city's two football squads, Genoa and Sampdoria, who have postponed their weekend matches.