President Jacob Zuma's remark earlier in the week about the majority ruling in a democracy were "misconstrued", the presidency said on Sunday.
"President Zuma wishes to remind those who were concerned by the remarks that South Africa is a constitutional democracy and the rights of all citizens are guaranteed in the Constitution," his office said in a statement.
"All South Africans are equal, regardless of colour, race or creed."
The presidency said the Democratic Alliance had misconstrued Zuma's remark to mean that the minority had fewer rights. This was not the case, his office said.
Zuma had been stating a fundamental democratic principle, that while all members of society had opinions, the will of the majority carried the day.
"There is, therefore, nothing untoward or incorrect in what the president said in his response to a question about trade unions in Marikana when answering questions in Parliament," the presidency said.
Zuma told Parliament on Thursday that the majority ruled in a democracy.
"You have more rights because you're a majority; you have less rights because you're a minority. That's how democracy works," he said.
In a statement on Sunday, Mazibuko dismissed the presidency's comments on the matter as a "desperate attempt at damage control".
"President Zuma has again revealed himself as someone who fails to understand the basic pillars of our constitutional democracy...
"This is a president who does not believe the constitution is above the ANC. In his mind, it is only there to serve the ANC," she said.
As president, Zuma had a duty to protect the Constitution, which he swore to uphold when taking office.
"The DA therefore reiterates our call for the president to unconditionally retract his comments immediately."
When Zuma made the remark he was responding to a question from Mazibuko, on whether he would consider changes to the labour relations regime, which pegged the union representation threshold at 51 percent.
At the time, she said this had led to the situation where Amcu (the Association of Mineworkers and Construction Union) was not a recognised union at Lonmin's platinum mine, and was therefore excluded from wage negotiations.
This had empowered "the ANC-affiliated National Union of Mineworkers" to establish a monopoly at the mine.
"Does the president believe that smaller unions should be empowered to negotiate on behalf of their members, and not be excluded by big unions like NUM, in a winner-takes-all scenario?.
"Would this not avert tension and the possible violence now posing a threat to South Africa's mining sector?" Mazibuko asked.
The president said workers who did not join the majority union could not expect the same privileges.
"Workers who do not join the union, can't have the same kind of privileges... You can't have a union of half-a-dozen people [and say] because they've declared it a union, you must have the same rights.
"In a democratic situation, it is the majority that prevail. I can't change the rules because you want to make a particular point. You can't then say, smaller unions must then be compared to the bigger unions in the same way."
Zuma told MPs it was "a question of accepting the rules of democracy, and operating within them".
An unidentified MP responded from the opposition side of the House: "You don't understand democracy."