Whether ANC president Jacob Zuma served two terms was "none of Cosatu’s business," Mantashe told the paper.
"It cannot be the decision of Cosatu on whether he takes 20 terms or two. That is the decision of the branches of the ANC," said Mantashe.
On Thursday, Cosatu general secretary Zwelinzima Vavi said Zuma would serve two terms as ANC president.
"We know the president said only one term, but we have engaged with him," said Vavi.
"It is no longer on the table. He will run two full terms."
Mantashe told the Sunday Times that Vavi and Cosatu had no basis to speak on the ANC’s leadership succession.
"Cosatu is going to its own conference [in September]. The ANC is not issuing a statement that Vavi should not go for a fourth term, or whatever," said Mantashe.
Cosatu president S’dumo Dlamini told the paper that Mantashe had contacted the union to voice his criticisms.
"His main concern was that the ANC had not discussed the matter. He also raised concerns that Cosatu had gone public with this matter before it is discussed in the ANC," said Dlamini.
"We have accepted the fairness of his concerns."
Vavi was responding to a reporter’s question about the succession issue in 2012 when he made the comments about Zuma’s two terms.
"The issue of succession does not even arise. That discussion is not arising in 2012 as far as we are concerned," said Vavi.
Dlamini told the Sunday Times that Vavi was not speaking about the ANC’s succession but that of the state president.
"We are not saying Zuma should take two terms as ANC president. We are referring to his two terms as state president," said Dlamini.
"We are not talking about succession in the ANC. We are talking about the state president. Alliance partners cannot be barred from talking about that issue."
On Friday, Zuma told the SABC that whether or not he serves a second term as ANC president would be left to his party. – Sapa