By Steve Scherer and Gabriele Pileri

PESCARA DEL TRONTO, Italy (Reuters) - Hopes of finding more survivors from Italy's powerful earthquake faded on Friday, with the death toll rising to 281 and the rescue operation in some of the stricken areas called off.

Three days after the quake struck the mountainous heart of the country, sniffer dogs and emergency crews continued to scour the town of Amatrice, which was leveled in the disaster, but there was no sign of life beneath the debris.

"Only a miracle can bring our friends back alive from the rubble, but we are still digging because many are missing," town mayor Sergio Pirozzi told reporters.

In nearby villages, such as Pescara del Tronto, rescuers pulled out after all the inhabitants had been accounted for.

Italy plans to hold a state funeral for around 40 of the victims on Saturday, which will be held in the nearby city of Ascoli Piceno. A day of national mourning was announced, with flags due to fly at half mast around the country for the dead, who include a number of foreigners.

The civil protection department in Rome said 388 people were being treated for injuries in hospitals, and 40 of them were in critical condition. An estimated 2,500 people were left homeless by the most deadly quake in Italy since 2009.

Survivors with nowhere else to go are sleeping in neat rows of blue tents set up close to their flattened communities. The government has promised to rebuild the region, but some local people feared that would never happen.

"I'm afraid our village and others like it will just die. Most people don't live here year round anyway. In the winter time the towns are virtually empty," said Salvatore Petrucci, 77, who came from the nearby hamlet of Trisunga.

"We may be the last ones to have lived in Trisunga."

More than 1,050 aftershocks have hit the area since the 6.2 magnitude quake early on Wednesday, bringing fresh damage to structures still standing. These included a bridge leading to Amatrice, which had to be closed on Friday, further complicating the rescue operation.

The original quake was so strong that the town nearest the epicenter, Accumoli, sank by 20 cm (7.87 inches), according to Italy's geological institute.

FOREIGN VICTIMS

By Friday, most of the outlying communities were quiet and empty, buildings lying in crumpled mounds, the innards of private homes exposed to the skies and belongings scattered in the debris.

"We have removed the last bodies that we knew about," said Paolo Cortelli, a member of the Alpine Rescue national service who helped to recover about 30 bodies from Pescara del Tronto.

"We don't know, and we might never know, if the number of missing that we knew about actually corresponds to the people who were actually under the rubble."

The foreigners who died in the disaster included six Romanians, a Spanish woman, a Canadian and an Albanian. Three British holidaymakers, including a 14-year-old boy, also died.

The area is popular with vacationers and local authorities were struggling to pin down how many visitors were present when the quake hit.

The Romanian Foreign Ministry said 17 Romanians were still missing. Italy has a large Romanian community, and some of the victims were residents in the country.

The first funeral of a victim was held in Rome on Friday, for Marco Santarelli, the 28-year-old son of a senior state official, who died in the family's holiday home in Amatrice.

"I cannot find the words to describe the grief of a father who outlives his own children. Perhaps there are no words," Marco's father, Filippo Santarelli, told Corriere della Sera newspaper.

Later in the day, a funeral service for six other victims, including an 8-year-old boy and two girls aged 14 and 15, was held in their hometown of Pomezia, south of Rome.

Officials said 181 of the victims had been identified, including at least 21 children. The youngest was just 5-1/2 months old. The eldest was 93.

RAZED

Hardly a single building was left unscathed in Amatrice, which was last year voted one of the most beautiful old towns in Italy and is famous for its local cuisine.

"Amatrice will have to be razed to the ground," said mayor Pirozzi, who urged youngsters not to leave the area, saying that would mean the end of their community.

"No night can last so long that the sun never rises again. I am convinced that Amatrice will rise again. We owe it to the people who died here."

Prime Minister Matteo Renzi has declared a state of emergency for the region, allowing the government to release an immediate 50 million euros ($56 million) for the relief work.

He has promised to rebuild the shattered homes and said he would also renew efforts to bolster Italy's flimsy defenses against earthquakes that regularly batter the country.

"We want those communities to have the chance of a future and not just memories," he told reporters in Rome on Thursday.

Italy has a poor record of rebuilding after quakes. About 8,300 people who were forced to leave their homes after a deadly earthquake in L'Aquila in 2009 are still living in temporary accommodation.

This latest disaster represents a major political challenge for Renzi, who has been in office for two-and-a-half years. Former prime minister Silvio Berlusconi was widely criticized for what was perceived to be a botched response to the L'Aquila calamity.

Renzi called for national unity and declined to predict when the homeless might be rehoused. "This is not about setting challenges and making promises. We need the pace of a marathon runner," he said.

Insurance association ANIA estimates that less than one percent of Italy's 33 million homes have private quake coverage, meaning the bill for insurance companies was likely to be low.

That means that the reconstruction bill will have to be paid by the heavily indebted state. Infrastructure Minister Graziano Delrio said on Friday he did not think rebuilding costs would reach the 14 billion euros earmarked for L'Aquila.

Most of the buildings in the Amatrice area were built hundreds of years ago, long before any anti-seismic building norms were introduced, helping to explain the widespread destruction.

Cultural Minister Dario Franceschini said all 293 culturally important sites, many of them churches, had either collapsed or been seriously damaged.

Italy sits on two fault lines, making it one of the most seismically active countries in Europe. Almost 30 people died in earthquakes in northern Italy in 2012 while more than 300 died in the L'Aquila disaster.

(Additional reporting by Rome newsroom; Writing by Crispian Balmer and Philip Pullella, editing by David Stamp)