Ramaphosa addressed the nation Monday evening, calling for calm after at least six people died in the violence and hundreds were arrested.
As Zuma’s lawyers argued for a sentence reduction Monday, protests and looting centered in two provinces escalated.
“We will not hesitate to arrest and prosecute those who perpetrate these actions and ensure they face the full might of the law,” Ramaphosa said in a national address, as local media played live pictures of malls being looted in Durban.
“It is this rule of law that enables our society to function and our economy to develop in the interests of the people of South Africa.”
Ramaphosa acknowledged the protests and looting may have begun with political grievances, but that criminal elements had taken over.
“What we are witnessing now are opportunistic acts of criminality,” he said.
“We will soon be facing a huge risk of food insecurity and medication insecurity in a few weeks. Our vaccination program has been severely disrupted just as it is gaining momentum,” he said.
His remarks come just 24 hours after he extended the country’s lockdown by another two weeks.
CNN witnessed police firing rubber bullets at dozens of looters as they ran from a mall with everyday items, while other shops in the vicinity were set ablaze.
He handed himself over to police last week to begin his jail term after days of speculation over whether he would comply with the court’s orders.
Zuma’s conviction marks a fall from grace for the former leader, who served as president from 2009 to 2018 and was once widely celebrated as key figure in the country’s liberation movement. Zuma spent 10 years in prison with anti-apartheid hero and former President Nelson Mandela.
CNN’s Sarah Dean, Vasco Cotovio, Lindsay Isaac and Angela Dewan contributed to this report.