The death toll from South Africa's "unprecedented" floods climbed to 341 as helicopters fanned out across the southeastern city of Durban in an increasingly desperate search for survivors.

With roads and bridges washed away by freak rainfall this week, rescuers battled to deliver supplies across the city, where some residents have been without power or water since Monday.

"The level of devastation of human life, infrastructure, and service delivery network in the province is unprecedented," said Sihle Zikalala, the premier of KwaZulu-Natal province.

"A total number of 40,723 people have been affected. Sadly, 341 fatalities have been recorded," he told a news conference.

At a small airport north of Durban, helicopters carried rescuers in and out. The air support was pulled from military and police, but also a fleet of volunteers, private contractors and schools.

But one day after the rains finally subsided, fewer survivors were being found, said Travis Trower, a director for the volunteer-run organisation Rescue South Africa.

Residents of Quarry Road informal settlement wash their clothes as others rebuild their home

From 85 calls today, he said his teams had found only bodies.

"It's unfortunate, but we do the best we can for as many people as we can," he said.

The government has given no indication of how many people are missing.

Mr Zikalala predicted that the bill for damage will run into billions of rand (hundreds of millions of euros).

Appeal for shelter

President Cyril Ramaphosa has declared the region a state of disaster to unlock relief funds.

Authorities said they had established 17 shelters to accommodate over 2,100 displaced people.

Sporadic protests erupted in some areas over slow restoration of services and a lack of relief. Durban's city government appealed for patience.

"We understand the frustration and anxiety of our residents," it said in a statement.

"We are working as quickly as we can. Our teams are hard at work to resume services. However, it may take a while to fully restore all services because of the extent of the damage to access roads."

The government of KwaZulu-Natal province has also put out a public call for aid, urging people to donate non-perishable food, bottled water, clothes and blankets.

But many survivors said they had been left to fend for themselves.

Residents collect clean water from a broken pipe in Amaoti

In Amaoti, a township north of Durban, residents balanced precariously on the embankment of a collapsed road, trying to fetch clean water from a broken pipe underneath.

"We don't have water, there is no electricity... people from (everywhere) are coming to get water," Thabani Mgoni, 38, told AFP in the midst of the crowd.

Philisiwe Mfeka, a 78-year-old grandmother, said her water supply stopped on Tuesday.

Even water from the fractured pipe was being rationed to one bucket per person, with children, some as young as ten, coming to fetch one bucket each.

At a riverside, families washed what clothes they could recover in muddy water, amid severed pipes that poked from earth.

Brutal storm

In a pitch-dark hall in Durban's Glebelands, volunteers in a dingy apartment block used mobile phone torches to illuminate their registration of scores of displaced people overnight.

"We are just helping the people because we care," said Mabheki Sokhela, 51, who helped organise temporary shelter at a community hall.

He urged fellow residents to shelter the victims. "There is not enough space," he said.

Residents stand on a collapsed bridge north of Durban

Many victims slept on chairs or on cardboard on the floor.

Weather experts say apocalyptic levels of rain were dumped on the region over several days.

Some areas received more than 450mm (18 inches) in 48 hours, amounting to nearly half of Durban's annual rainfall of 1,009mm, the national weather service said.

The South African Weather Service has issued an Easter weekend warning of thunderstorms and localised flooding in KwaZulu-Natal and neighbouring Free State and Eastern Cape provinces.