At least 45 people have now died in the violence that has been engulfing parts of South Africa since the jailing of former President Jacob Zuma last week.
This includes 10 people killed in a stampede during looting on Monday night at a shopping centre in Soweto, the country's biggest township.
Almost 800 people have been arrested in the unrest that began last Thursday and turned violent over the weekend.
The military has now been deployed to help the overstretched police.
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 looted in major cities and small towns in KwaZulu-Natal and Gauteng provinces.
Police Minister Bheki Cele told journalists on Tuesday that, if the looting continued, there was a risk areas could run out of basic food supplies.
However, Defence Minister Nosiviwe Mapisa-Nqakula said there was not yet a need to declare a state of emergency over the violence.
KwaZulu-Natal Premier Sihle Zikalala said some 26 people had been killed in the province so far. In Gauteng the death toll is 19, including the 10 who died at the mall in Soweto.
The BBC's Vumani Mkhize says several shopping centres in the township - once home to Nelson Mandela - have been completely ransacked with ATMs broken into, restaurants, bottle stores and clothing shops all left in tatters.
Soldiers, working with the police managed to catch a few rioters, but law enforcement remains heavily outnumbered, he says.
In KwaZulu-Natal - where livestock has also been stolen - the unrest continues with ambulances even coming under attack by rioters in some areas, South Africa's TimesLive news site reports.
Officials have accused some groups of taking advantage of the anger over Zuma's imprisonment to commit criminal acts, while others have said anger over unemployment and poverty are fuelling the chaos.-BBC