The bitterly cold winter storm struck the largely rural and underdeveloped province on Monday, causing a river to burst its banks and submerge homes, with several make-shift dwellings toppled.

The worst-hit area was around the city of Mthatha, about 800 kilometres (500 miles) south of Johannesburg, where residents picked through the mud three days later to salvage what they could from their destroyed homes.

AFP journalists saw a rescue team pull four bodies, some of them children, from a one-roomed house in the late afternoon as locals watched.

Houses, trees and cars were covered in mud and fields were strewn with debris.

"As the water subsides, more bodies are being discovered," said Caroline Gallant, Eastern Cape manager at the South African Red Cross Society, which has sent assistance to the disaster zone.

More than 3,000 houses have been affected, she told AFP, adding it was "the worst ever disaster" recorded in the area.

"The figure has gone to 78," Velenkosini Hlabisa, minister of cooperative governance and traditional affairs, told public broadcaster SABC News.

These include six school students who were among 10 in a school van that was swept away in the flooding, he said. Four of the children are still missing, officials said.

"We learnt of an additional two learners today... who have been confirmed as having died on the walk to school," Basic Education Minister Siviwe Gwarube said.

"We are reeling," she told the SABC.

Ali Sablay, a spokesperson for disaster response charity the Gift of the Givers Foundation, said Thursday evening their teams had recovered eight new bodies, including three children.

President Cyril Ramaphosa called the floods "unprecedented" and said he would visit the disaster-hit region Friday.

- Door to door -

One rescuer, who spoke to AFP on Thursday on the condition of anonymity as he was not allowed to speak to the media, said his team was expecting to find more bodies and possibly survivors.

"We are going door to door to see, because yesterday we did find people locked inside houses who couldn't get out and were deceased," he said.

The storm damaged power and water supplies and at least 600 people have been displaced, the provincial government said, with many sheltering in community halls.

Infrastructure has also been damaged and at least 20 health facilities affected, the local authority said.

"The numbers will increase dramatically," Sablay said.

"In the last 24 hours the number of people requiring assistance has jumped from 5,000 to 10,000," he told AFP.

"The homes are fragile, they can collapse any time; food is contaminated so people need to be evacuated," he added.

The government urged South Africans to be vigilant over the next few days as more "extreme weather" was expected across the country.

The province -- where Nelson Mandela was born -- is among the poorest in the country, with 72 percent of people living below the poverty line, according to the Southern African Regional Poverty Network.

Snow and heavy rainfall are common during winter in South Africa but the country is also highly vulnerable to the impact of climate variability and change, which increases the frequency and severity of droughts, floods and wildfires, according to the Green Climate Fund.

"We must take a tough stance that everyone who is living on a flood plain must be removed," minister Hlabisa said. "Climate change is a reality now."