The ANC did not say what had been decided at the meeting between Zuma and the party's "Top Six" leadership team at Zuma's residence in Pretoria, but it summoned its National Working Committee (NWC) to an urgent meeting on Monday afternoon.
Zuma, who is battling corruption allegations, has been in a weakened position since he was replaced as leader of the ANC in December by Cyril Ramaphosa, the deputy president.
Sources said this was to help avoid accusations of conflict of interest being levelled against Ramaphosa because he was expected to take over from Zuma as soon as Zuma stepped down.
Zuma could leave office either by resigning, through losing a motion of no-confidence in parliament or impeachment proceedings.
EFF president Julius Malema has requested that the motion of no confidence against President Jacob Zuma on February 22 be held through a secret ballot.
ANC defenders under the banner of #DefendLuthuliHouse have vowed to form a human chain around the party's headquarters in Johanensburg to stop protesters marching in support of Zuma. "That is why tonight [Sunday] we are meeting with President Zuma", Mantashe said.
His hold on the ANC was shaken when his chosen successor - his former wife Nkosazana Dlamini-Zuma - lost out to Ramaphosa in the closely-fought race to be party leader.
The on and off announcements of the president stepping down have proven to have a strong effect on South Africa's markets, with every bit of news pointing to an early exit giving the rand a boost, followed by a small drop after reports are dismissed.
He is due to deliver a speech at the opening of parliament in Cape Town on Thursday.
A call by the Democratic Alliance to delay the Sona was this week rejected by National Assembly Speaker Baleka Mbete‚ who said it was not allowed under parliamentary rules.