This includes 10 people killed in a stampede during looting on Monday night at a shopping centre in Soweto.
The BBC filmed a baby being thrown from a building in Durban that was on fire after ground-floor shops were looted.
The military has now been deployed to help the police overstretched since the unrest began last week.
South African police said in a statement that they had identified 12 people suspected of provoking the riots, and that a total of 1,234 people had been arrested.
President Cyril Ramaphosa has called it some of the worst violence witnessed in South Africa since the 1990s, before the end of apartheid, with fires set, highways blocked and businesses and warehouses looted in major cities and small towns in KwaZulu-Natal and Gauteng provinces.
Ministers have warned that if looting continues, there is a risk areas could run out of basic food supplies soon – but have ruled out declaring a state of emergency.
What happened to the baby?
The child was caught by a crowd of people who rushed to help those trapped in the apartment block in the central business district of Durban, a coastal city in KwaZulu-Natal, on Tuesday afternoon.
Those stealing from shops on the ground floor of Smith Street had started the fire which spread, affecting those living upstairs.
The BBC’s Nomsa Maseko says that after catching the baby, the passers-by and neighbours rushed to get ladders to help other residents, including children, escape.
The mother was reunited with her baby, but was too emotional to talk. The rescue services arrived after about 20 minutes to help dowse the fires.
How bad is the damage?
More than 200 shopping malls had been looted by Monday afternoon, Bloomberg news agency quoted the chief executive officer of Business Leadership South Africa, Busisiwe Mavuso, as saying.
Several shopping centres in Soweto – South Africa’s largest township which was once home to Nelson Mandela – have been completely ransacked, with ATMs broken into, restaurants, stores selling alcohol and clothing shops all left in tatters.
Soldiers working with the police managed to catch a few rioters; in total almost 800 have been arrested, but law enforcement remains heavily outnumbered, he reports.
In KwaZulu-Natal – where livestock has also been stolen – the unrest continues with ambulances coming under attack by rioters in some areas, South Africa’s TimesLive news site reports.
Video footage shows that a blood bank was looted in Durban as Mr Ramaphosa addressed the nation on Monday night.
