Flash floods have swept through several towns in hilly central Italy after hours of exceptionally heavy rain, leaving 10 people dead and at least four missing.

Dozens of survivors scrambled onto rooftops or up trees to await rescue.

Floods invaded garages and basements and knocked down doors.

In one town, the powerful rush of water pushed a car onto a second-storey balcony, while elsewhere parked vehicles were crumpled on top of each other in the streets.

Some farm fields near the sea were metres under water.

“It wasn’t a water bomb, it was a tsunami,” Riccardo Pasqualini, the mayor of Barbara, told Italian state radio of the sudden downpour on Thursday evening that devastated his town in the Marche region, near the Adriatic Sea.

He said the flooding left the 1,300 residents of Barbara without drinking water.

A mother and her young daughter were missing after trying to escape the floods, the mayor told Italian news agency ANSA.

Elsewhere in the town, a boy was swept away from the arms of his mother, who was rescued.

Premier Mario Draghi told a news conference in Rome that 10 people were dead and four were missing in the flash floods. He thanked rescuers “for their professionalism, dedication and courage”.

Officials said some 50 people were treated at hospitals for injuries.

Mr Draghi, who is serving in a caretaker role ahead of Italy’s national election on September 25, planned to tour some devastated towns and his government announced five million euros in aid to the region.

“It was an extreme event, more than an exceptional one,″ climatologist Massimiliano Fazzini told Italian state TV. He said, based on his calculations, the amount of rain that fell, concentrated over four hours that included an especially heavy 15-minute period, was the most in hundreds of years.

In a space of a few hours, the region was deluged with the amount of rainfall it usually receives in six months, state TV said. A summer of virtually no rain meant hillsides were unusually hard and dry, so the water ran faster down the slopes, increasing its impact.

The fire department tweeted that dozens of people who were trapped in cars or had clambered up to rooftops or climbed trees to escape rising floodwaters had been brought to safety.

Police officers in the town of Sassoferrato recounted the rescue of a man trapped in a car. Unable to reach him, they extended a long branch, which the man grabbed onto and then officers pulled him to safety.

Helicopter crews rescued seven people in remote towns of the Apennine Mountains.

Hundreds of firefighters struggled to remove toppled tree trunks and branches amid thick mud as they searched for people who could have been buried by debris. They waded through waist-high water in flooded streets, while others paddled in rubber dinghies to scoop up survivors.

In the town of Ostra, a father and his adult son were found dead in their building’s flooded garage where they had gone to try to get their car out, and another man who tried to remove his motorcycle from a garage also died, state TV said. Elsewhere, a man was found dead in his car.

“As it (the flood) played out, it was far, far worse than forecast,” said Civil Protection chief Fabrizio Curcio. A bad weather watch had been issued on Thursday, but not at the highest level.

Hundreds of people fled or were evacuated from their homes until the premises could be checked for safety and mountains of mud cleared away.

Some of the worst flooding hit the town of Senigallia, where the River Misa overflowed its banks.

Hamlets in the hills near the Renaissance tourist town of Urbino were also inundated when fast-moving rivers of water, mud and debris rushed through the streets.