Large crowds packed inside an exhibition hall turned into a makeshift chapel where coffins adorned with flowers and photographs were lined up, although the families of some victims shunned the state event.
"I lost a friend but I came for all the victims," local resident Nunzio Angone told AFP.
Italian President Sergio Mattarella and Prime Minister Giuseppe Conte presided over the hour-long Catholic service, which coincided with a national day of mourning for Tuesday's disaster.
A visibly shaken Mattarella spoke of an "unacceptable tragedy".
The death toll now stands at 43 including several children after the discovery Saturday of the body of a labourer in his 30s in the rubble and the death of another man in hospital, officials said.
Local media reported that the bodies of three family members, including a nine-year-old girl, had also been found inside a car under debris.
At the ceremony, there was applause as a priest read out the names of the dead.
"The Morandi bridge collapse has pierced the heart of Genoa. The pain is deep," Archbishop Angelo Bagnasco said.
Solemn chants of "Allahu akbar" (God is greatest) then rang out as an imam led prayers for two Muslim victims.
His presence was particularly poignant in a staunchly Catholic country, where the far-right is now in power and which has seen a rise in attacks on foreigners.
Rigorous investigation
The populist government has blamed Autostrade per l'Italia, the operator of the viaduct, for the collapse and wants to strip the company of its lucrative contracts.
Autostrade chief executive Giovanni Castellucci said at a press conference that 500 million euros will be available from Monday to help Genoa and to rebuild the bridge while funds would be set up to help victims.
The government has accused the infrastructure giant of failing to invest in sufficient maintenance.
Interior Minister Matteo Salvini had demanded that the company offer up to 500 million euros to help families and local government deal with the aftermath of the disaster.
The government was set to hold an emergency meeting in Genoa on the disaster later on Saturday.
"Everyone who has come here in recent years has gone over that bridge. I have travelled along that bridge many times too, also recently," Mattarella said, vowing to carry out a "rigorous investigation" into the accident.
"Farce of a funeral"
Relatives of victims comforted each other as they huddled around each of the 19 caskets.
Among the coffins was a small white one for the youngest victim, an eight-year-old boy who was killed alongside his parents as they prepared to catch a ferry to the holiday island of Sardinia.
"I don't know those who have died in the bridge collapse but I wanted pay my respects regardless. This shouldn't have happened," Genoa resident Claudio Castellaro, 73, told AFP.
Applause erupted as firefighters entered the hall ahead of the ceremony.
There was also loud clapping for co-deputy premiers Matteo Salvini and Luigi di Maio who have led angry tirades against Autostrade.
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 that has provoked this; let them not show their faces, the parade of politicians is shameful," the press quoted the mother of one Italian victim as saying.
Roberto, father of another victim, 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."
Riddled with problems
The Morandi viaduct dates from the 1960s and has been riddled with structural problems for decades, leading to expensive maintenance and severe criticism from engineering experts.
Its collapse prompted fears over ageing infrastructure across the world.
Italy has announced a year-long state of emergency in the region.
Autostrade, which operates and maintains nearly half of Italy's motorways, estimates it will take eight months to build a new steel bridge, according to Castellucci.
It denies scrimping on motorway maintenance, saying it has invested over one billion euros a year in "safety, maintenance and strengthening of the network" since 2012.
Atlantia, the holding company of Autostrade which is 30 per cent owned by iconic fashion brand Benetton, has warned that the government would have to refund the value of the contract, which runs until at least 2038.
