Italy on Tuesday held a poignantly symbolic funeral for victims of last week's earthquake amid the ruins of Amatrice, the small town that bore the brunt of the disaster.

President Sergio Mattarella, Prime Minister Matteo Renzi and a senior representative of Pope Francis were among hundreds of mourners at the service on the edge of the hilltop beauty spot where 231 of the quake's 292 confirmed fatalities occurred.

The coffins of nearly 40 of them were laid out for a service held just yards from piles of collapsed masonry, a hastily-constructed temporary structure allowing the solemn funeral mass to proceed under cover from the rain.

The venue was a last-minute decision after grieving locals reacted with fury to a proposal for the funeral to be held in an aircraft hangar in the main town in the district, Rieti, some 40 miles (64 kilometres) away.

The drizzle provided a reminder of how soon summer will turn to chilly autumn in this remote, mountainous area of central Italy, making life even more uncomfortable for hundreds of homeless residents facing an indefinite stay in tented villages erected to house them.

Also presented in Amatrice were Rome mayor Virginia Raggi, paying her respects to the more than 80 residents of the capital who died, and Romanian Prime Minister Dacian Ciolos.

At least 11 Romanian nationals died in the quake, most of them in Amatrice.

Most of those who died had already been buried in private family seminars or after a first state funeral in Ascoli Piceno on Saturday.

The bishop of Rieti, Domenico Pompili, presided over Tuesday's ceremony, urging the leaders present not to allow reconstruction to get bogged down in "political quarrels."

"If we abandon these villages, we will kill them for a second time," the bishop said.

- Mourning over, probe starts -

With the public acts of mourning completed, the focus will now shift to helping survivors deal with the aftermath of the disaster and answering numerous questions about why it had such a deadly impact.

For the Civil Protection agency, the top priority is providing adequate shelter for some 2,900 people who are without permanent accommodation barely two months from the onset of what is often a severe winter.

The issue of where local children will be educated is also pressing with the autumn term due to start by the middle of September at the latest.

Local prosecutor Giuseppe Saieva meanwhile has opened an investigation into whether any criminal responsibility can be accorded for the deaths.

His culpable homicide/culpable disaster probe will notably focus on whether authorities were negligent in ensuring the upgrading of public and other buildings to modern anti-quake norms in the aftermath of the 2009 earthquake in nearby L'Aquila.

He will also examine whether property owners side-stepped building regulations when undertaking extension or renovation work on what are often centuries-old buildings.

The first concrete move in the probe came on Tuesday with the issuing of a sequestration order related to an Amatrice elementary school which collapsed in the quake despite having been subject to an expensive anti-quake upgrade only a few years earlier.

The National Anti-Corruption Agency (ANAC) is also looking into what happened at the Romolo Capranica school. Its boss Raffaele Cantone on Tuesday ordered police to seize all documents related to the tender for the renovation work.

Saieva, who attended Tuesday's ceremony, admitted he could not rule out the possibility of ordinary residents who might have lost their homes or even loved ones facing criminal investigation, if they had ignored safety rules.

"That could be, we will have to see," he told the Sky TG24 news channel. "If they didn't do it (observe building rules) buildings collapse."