The African National Congress (ANC) had called a special meeting of its executive committee for Wednesday in Cape Town, possibly heralding a bid to unseat the 75-year-old leader, who is beset by corruption allegations and damaged by an economic decline.
Mr Zuma has been in a weakened position since he was replaced as leader of the ANC by Deputy President Cyril Ramaphosa in a vote in December.
The President no longer holds a top position in the party, which has faced uncertainty over how its dual power structure will function.
Mr Zuma’s tenure as President officially runs until mid-2019.
The scheduled meeting of the National Executive Committee, which has the power to demand that Mr Zuma step down, was expectedly moved on Tuesday to the weekend of 17 February.
Party Secretary-General Ace Magashule said the meeting had been put back to allow the President and Mr Ramaphosa to keep talking constructively on a transition.
South Africa’s The Times, citing unnamed sources, said Mr Zuma would resign “as soon as a list of preconditions has been finalised” by the two men.
Mr Magashule, who attended the meeting between the two leaders, would not confirm whether Mr Zuma had agreed to resign, although other ANC leaders said the agreed deal would see the President “go in a dignified way”.
Mr Zuma has been South Africa’s most controversial president since the end of white minority rule in 1994, enwrapped in scandal during a tumultuous nine years in power.
He has faced multiple allegations of corruption. Some within the ANC and the opposition say the Gupta family, an Indian-born businessmen who are friends of Mr Zuma, have used their links with the president to win work with the state. The Guptas and Mr Zuma have denied any wrongdoing.
Cyril Ramaphosa became the ANC's President at an elective conference in Johannesburg in December (AP)
Mr Zuma waved to reporters after meeting Mr Ramaphosa at his office in Cape Town, where the President also chaired routine meetings, his spokesman said.
In a statement, the Presidency denied claims by the South African Communist Party, a key ally of the ruling party, that Mr Zuma was preparing to fire Mr Ramaphosa as Deputy President and replace him with ex-wife, Nkosazana Dlamini Zuma.
The ANC had earlier heavily flagged Wednesday’s scheduled meeting of its leaders by saying they would decide a “matter of serious concern.”
Mr Zuma is facing a no-confidence vote in parliament on 22 February. He has survived several attempts to oust him in the past, but this time around a significant part of the ANC wants him to step down well before his second term ends next year.
“A vote of no-confidence is not desirable, under any circumstances,” ANC Deputy Secretary-General Jessie Duarte told a news conference.
She added: “Our most important consideration is that we don’t believe South Africa should wish for us to embarrass the President of the republic, in any way whatsoever.”
The speaker of parliament, Baleka Mbete, postponed a speech Mr Zuma had been due to give on Thursday, though she said a new date would be fixed soon.
Opposition parties have demanded that the speech be postponed until Mr Zuma was removed from the leadership.
The rand, which has tended to strengthen on signs that Mr Zuma could step down before his second term as president ends next year, was firmer on Tuesday.
The ANC’s top six most powerful officials met Mr Zuma late on Sunday at his official residence in Pretoria. There was no announcement of the outcome though sources told Reuters he had refused a demand to go.
Mr Zuma has also resisted a call to go by Zulu King Goodwill Zwelithini, the influential head of South Africa’s biggest ethnic group in the President’s home province of KwaZulu-Natal, according to the newspaper Business Day.
The influential Nelson Mandela Foundation said in a statement that “time is of the essence – Zuma must go”.
Leader of the official opposition and head of the Democratic Alliance party Mmusi Maimane added: “We need a new beginning.”
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