The meeting of the party's National Executive Committee (NEC), which has the power to demand that Zuma step down, raises the prospect of a decisive showdown between the 75-year-old allies and those who want Ramaphosa to take over from him now as president.
ANC National Chairperson Gwede Mantashe opens proceedings at the Mandela centernary celebrations in Cape Town.
The uncertainty about Zuma's fate as president has left the country in limbo with opposition parties, alliance partners and some in the ANC calling for his removal.
According to our information, Ramaphosa ended his negotiations, or "talks to manage the transition", with Zuma and called an urgent meeting of the ANC's Top Six (president, deputy president, chairperson, secretary-general, deputy secretary-general and treasurer) to report to them on the impasse.
Zuma's hold over the ANC was shaken in December when his chosen successor - ex-wife Nkosazana Dlamini-Zuma - narrowly lost out to Ramaphosa in a vote for new party leader.
"The centenary of the birth of Nelson Mandela gives us an opportunity for renewal and rebuilding", Mr Ramaphosa said, noting that the party and the county was emerging from a hard period.
"The National Executive Committee will be doing precisely that".
Down but not out- yet South Africa's embattled President Jacob Zuma has rejected a party request that he resign
Mr. Zuma hasn't publicly commented on the most recent push to remove him.
Sunday's rally was part of ANC celebrations marking 100 years since Mandela's birth - as well as efforts by Ramaphosa to fix the party's reputation ahead of next year's general election. "That is what Nelson Mandela would have wanted".
The decision to convene the meeting in the capital, Pretoria, follows talks between the ANC's top six officials and Zuma on Saturday night to discuss the transition of power to the party's new leadership, said the people, who declined to be identified because of the sensitivity of the matter. "To do so, we will draw deeply on the wisdom of Nelson Mandela", he said.
"We just need to give them time to attend to these issues and in due time they will come back to us with solutions", he said in an interview.
So, if he so wishes, Mr Zuma can carry on as president of South Africa even if the NEC asks him to step down.
The party lost control of key municipalities in 2016 elections.