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"If that is the case, we will withdraw their registration. I will not even apologise for it," said Nzimande.
He said he would not allow a university to refuse admission - even on the grounds of language.
"There is unfortunately no place for racist institutions - no place. We will not allow such an institution."
Academia, which is associated with trade union Solidarity offers university education to students who wish to study in Afrikaans.
None of the historically Afrikaans universities - Pretoria, Stellenbosch, Free State, Potchefstroom, Johannesburg (previously Rand Afrikaans University) are exclusively Afrikaans.
In an interview with the Afrikaans language newspaper, Nzimande, who is also leader of the SA Communist Party, repeated his view that he wants universities to reflect a rainbow nation, with admission guaranteed, regardless of language.
He said it was not a stand against Afrikaans as a language, which he respected.
"It is our own language. We don't want to destroy it."
Solidarity chairman Flip Buys said they were not worried, because they were not guilty of what Nzimande claimed.
"I just do not like his PW Botha style of speaking."
