God cannot be blamed for the deadly earthquake that has devastated central Italy, a Catholic bishop said Tuesday, as he officiated a state funeral in Amatrice, the remote hilltop town worst hit by the tragedy.

Italian Prime Minister Matteo Renzi and President Sergio Mattarella joined the crowds at the evening service, held under a large canopy just outside the flattened town centre.

"God cannot be turned into a scapegoat" for what happened, the region's bishop said at the service.

"We should avoid accepting pathetic explanations, bordering on superstition, like blaming destiny, bad luck or striking coincidences," Rieti Bishop Domenico Pompili added.

"Without earthquakes, we would not have mountains and perhaps not even man and other forms of life. Earthquakes don't kill, the work of man does," Pompili said.

His words were likely an indictment of shoddy building standards. Earlier in the day, prosecutors in the provincial capital Rieti took Amatrice's elementary school under judicial administration after it collapsed despite renovations in 2012 that should have made it quake-proof.

Thirty-seven coffins, including two white ones for young children, were lined up for the funeral, attended by hundreds despite rainy weather. Each casket, bearing a name and a number, was covered with messages and flowers.

At the start of the service, the names of the dead were read out; towards the end, white ballons were released into the air.

A Jesus Christ figure was suspended above the altar, behind which laid a backdrop of collapsed buildings. A relic from the patron saint of Amatrice, the Madonna of Filetta, was retrieved from a damaged church and taken to the Mass.

Renzi visited survivors camped out in the Umbrian town of Amatrice before the funeral.

Romanian Prime Minister Dacian Ciolos was also in attendance. Eleven Romanians were among the quake dead, but they were not among the 37 given funeral rites, the Romanian embassy in Rome told dpa.

Some 242 people died in Amatrice and nearby Accumoli, but not all were given a state funeral. Families of other victims opted for private functions; many of those killed were tourists who were buried in their home towns, officials said.

Wednesday's magnitude-6 earthquake killed at least 292 people, including 50 in a third municipality, Arquata del Tronto. Thirty-five of its dead had a state funeral on Saturday, also attended by Renzi and Mattarella.

The calamity has left thousands of people homeless. Italy's civil defence agency, Protezione Civile, said more than 3,500 people slept overnight in makeshift camps. The number has increased steadily in recent days, as people stop sleeping in cars or in damaged homes.

On Monday there were fierce protests over a decision, later retracted, to move the Amatrice funeral to Rieti, out of practical considerations. Heeding complaints by survivors, Renzi aborted the plans.

That left the Protezione Civile less than 24 hours to deal with the logistical challenge of organizing a large ceremony in a half-destroyed town, with road access to it severely restricted due to quake damage.

In Amatrice, firefighters were still looking for people trapped under collapsed buildings, which were packed with tourists ahead of an annual festival for the local Amatriciana pasta dish. According to the ANSA news agency, 10 people are unaccounted for.

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