The Nelson Mandela Foundation has called for a discussion on the possible banning of the old national flag.
#BlackMonday protesters barricaded highways across the country last week to raise awareness over farm killings.
Some brandished the apartheid era flag.
The Nelson Mandela Foundation says that it spent a week reflecting on divisions in the country.
The foundation’s Luzuko Koti says: “We should think about it. Something must be done when people undermine symbols or the anthem of a country. We need to do it in a legal way to ensure the legacy of a country is not undermined.”
Meanwhile, Police Minister Fikile Mbalula says South Africans should rather be protesting against cop killings.
Mbalula says that police lowered their guard when protesters blocked highways to raise awareness around farm killings.
He says that crime affects all people, especially police, with 40 officers killed in the 2016/2017 financial year.
“I’ve never seen people marching for the murder of police officers. I’ve never seen people standing up to support police officers. Some are being killed on a daily basis.”