Ekurhuleni Mayor Mzwandile Masina on Monday warned white people and the civil organisation Save SA that things might get "very very rough".
Last Friday marches against President Jacob Zuma's recent Cabinet reshuffle, including one organised by Save SA in Pretoria, were held throughout the country.
"So please, we just want to request [Save SA] nicely: don't divide our nation because if you continue to do so those that sided with you in 1994, they won't be here in five years," Masina said.
"It might be very rough and we are many, this is not a threat, we are many [and] it might be very very rough."
"It is very important that we send a very very strong warning that... we will crush any individual who stands [in the way of] the project of nation building and social cohesion in South Africa."
Masina was the opening speaker at the Chris Hani memorial lecture at the Boksburg Civic Centre on Monday evening. Newly appointed Finance Minister Malusi Gigaba delivered the lecture.
Masina said the ANC would force white people to understand that they need to live in harmony with other South Africans.
'We are not monkeys, we are people'
"Now this thing of being shown the middle finger everywhere by white people because they've gained a new confidence must come to an end," he said to applause from the audience.
"I want to say to our white counterparts in South Africa, they must be very very careful.
"[They need to] understand that the issue of nation building and social cohesion requires all of us, not these insults that you get from social media and you get called everything else...that time has come to an end.
"...our children and your children, they don't see what you are seeing in us, we are not monkeys, we are people," he said.
Gigaba said South Africans should not forget the immense struggle by many to free South Africa.
"We should take care never to use their names to divide but to unite, never to destroy but to build," he said.
SA economy 'unsustainable'
Gigaba expressed concern over divisions within the ANC.
"We should call for a halt to divisions within the ANC. We are not properly managing disagreements in the ANC," he said.
Gigaba also said country's economy, from which the majority of South Africans are excluded, is unsustainable.
"We must agree on inclusion. South Africa's economy excludes black people, women and the youth. It's not sustainable," he said.
SACP leader Hani was killed at his home in Dawn Park, Boksburg, on April 10, 1993. A Polish far-right anti-communist immigrant, Janusz Walus, was later arrested for the murder.