Party leader Mmusi Maimane criticised the ANC of taking it's time to deal with the protests in North West and urged President Cyril Ramaphosa to listen to the people of Mahikeng and fire Mahumapelo immediately.
During the protests on Thursday, a man died, several buildings and vehicles were torched, and shops looted.
The SAHRC said it was concerning that the rights to assemble, demonstrate, picket and petition was being exercised in a manner that was in itself a violation of Section 17 of the constitution, which required that the exercise of this right must be peaceful and not pose harm to persons or property.
Residents in Mahikeng and surrounding villages went on a rampage on Wednesday, calling for North West Premier Supra Mahumapelo to resign.
The DA in North West said the ANC was protecting Mahumapelo, rather than intervening and alleviating the plight of communities in North West.
The police's Sabata Mokgwabone says, "We're managing the crowd... here and there, we're forced to use rubber bullets".
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Members of Nehawu have been on strike since 26 February, demanding the dismissal of head of the health department Dr Thabo Lekalakala, the termination of contracted companies by the department, bonus payments, payment of occupation specific dispensation (OSD) for employees at provincial offices and increase of community health workers' salaries.
"To pay attention to the situation in the North West, the president has chose to cut short his participation in the Commonwealth Heads of Government Meeting in London where he is leading a government delegation", a statement said.
He was due to address an urgent meeting in Mahikeng at 12pm (1000 GMT) alongside other senior ANC officials.
Zuma's nine-year tenure saddled South Africa with weak growth, ballooning national debt, depressed investor confidence and record unemployment.
Ramaphosa has vowed to crack down on government corruption, which he has admitted is a serious problem, and improve South Africa's ability to attract foreign investment.
Zuma appeared in court earlier this month at a preliminary hearing on graft charges that he denies.