Zuma's hold over the ANC was shaken in December when his chosen successor - his former wife Nkosazana Dlamini-Zuma - narrowly lost out to Ramaphosa in a vote to be the new party leader. However, he pulled out of the events, citing "other pressing commitments".
Speculation that Zuma's departure is imminent was fueled when Parliament postponed the annual state-of-the-nation address on Tuesday, two days before Zuma was to deliver it. Ramaphosa has said talks about a transition of power should conclude in a matter of days.
Addressing ANC supporters in Cape Town, Ramaphosa, who is deputy president, said: "The National Executive Committee of the ANC will be meeting tomorrow to discuss this very matter, and because our people want this matter to be finalised, the NEC will be doing precisely that".
"There is no disagreement about where we want to go (on Zuma) but the tactics on how to do that is the responsibility of leadership", Mantashe told the rally.
He said Ramaphosa had returned Gauteng province, where the ANC's headquarters is located in the country's commercial capital Johannesburg.
President Jacob Zuma could reportedly avoid prosecution on charges of state capture if he admits criminal wrongdoing, and enters into a deal with the state against the Gupta family.
She posted a happy photo of herself and her husband, seemingly inside a plane, from her Instagram account, firstladytzuma, with the following caption in isiZulu: "My crush, Nxamalala, Msholozi, Maphumephethe, Inkunzi, Emidiwayidwa, Zinyane likaMnyakanya".
The Democratic Alliance, the biggest opposition party, referred to unconfirmed media reports that Zuma demanded a state security detail for himself and his family as well as payment by the state of his legal fees.
As other users commented on the picture, she responded and said "Kuzoshuba ungalwi nomuntu ongalwi nawe", which loosely translated means: "It's going get rough, don't fight with someone who is not fighting you". He will finish what he started because he does not take orders beyond the Atlantic Ocean.
When Mandela finished, Ramaphosa briefly addressed the crowd.
"As we emerge from a period of difficulty, a period of disunity and discord, this Nelson Mandela centenary year offers us what I would call, a new beginning".
Zuma has been South Africa's most controversial president since the end of white-minority rule in 1994, overseeing a tumultuous nine years marked by economic decline and numerous allegations of corruption.
He still retains the support of a faction within the ANC but has seen several prominent party allies desert him recently.