Ramaphosa made the remarks when he visited Ethekwini Municipality, which includes the port city of Durban, one of the worst-hit areas in a week of looting that destroyed hundreds of businesses and killed more than 100 people.
"We obviously as a government are extremely concerned at what happened here and we are doing everything to deal with it, and it's quite clear that all these incidents of unrest and looting were instigated," Ramaphosa said.
"We will not allow anarchy and mayhem to unfold in our country," he said, adding that 25,000 soldiers would be deployed to flashpoints soon, up from 10,000 troops now.
He said the instigators had been identified and would be pursued by security agencies. One alleged instigator has already been arrested, a cabinet minister said on Thursday.
Calm was returning in parts of the main commercial city Johannesburg, even though most shops remain closed, and operations at the ports of Durban and Richards Bay were improving.
The rioting broke out in several parts of the country following the jailing of former President Jacob Zuma last week for his failure to appear at a corruption inquiry.
Ramaphosa also said he was concerned about rising racial tensions in some parts of the country.
