In an unannounced TV interview, 75-year-old president refused to quit, saying he had been given no reason by the party why he should resign.
"It was very unfair to me that this issue is raised... Nobody has ever provided the reasons. Nobody is saying what I have done." he said in the 45-minute long interview.
He said he would make another statement later today.
Addressing the media after an ANC Parliamentary Caucus meeting this afternoon, Mashatile said, "the ball is in his court. We can't wait. Its not fair to South Africans, the ANC or anybody."
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Mashatile said that if Zuma resigned by this evening, the motion of no confidence in Parliament would fall away.
"Should he resign, the cabinet stays and the Deputy President (Cyril Ramaphosa) takes over and we continue. However, if he doesnt resign and he is recalled, the whole cabinet goes. In that case the Speaker of Parliament will be the President until a new President is elected," Mashatile said.
"We had discussions between the officials of the ANC and President Zuma to find an exit for him where we did not want him to be humiliated. He has now chosen not to agree to (these discussions), so the National Executive Committee was left with no option but to recall him.
Zuma has previously survived several motions of no confidence by opposition parties in the past.