Ramaphosa, 65, joined Zuma's Cabinet as deputy in 2014 and replaced the president as head of the African National Congress in December, providing political cover for his increasing attacks on corruption at top levels of government.
The ANC national executive committee (NEC), which is the highest decision-making body in the party, was due to take a final decision on Zuma's future on Wednesday, but Ramaphosa dramatically cancelled the NEC meeting this week after what he called a "constructive and fruitful" meeting with Zuma on Tuesday.
Several thousand ANC supporters wearing the party's signature yellow, green and black colours attended the rally at the symbolic Grand Parade in central Cape Town.
Ramaphosa, an anti-apartheid activist who held the microphone for Mandela during the City Hall speech, was a key negotiator during the transition to democracy in the early 1990s.
Zuma seems to be staying out of the public eye.
On Tuesday, Parliament's presiding officers announced that Thursday's State of the Nation Address had been indefinitely postponed amid fears that it might descend into chaos.
He also acknowledged the disunity within the ANC but said Mr Mandela's centenary year "offers us a new beginning".
"We are in a very hard space, and there's no doubt it requires a great deal of courage and moral strength to pass this moment", ANC deputy secretary general Jessie Duarte said Sunday.
This, however, has not gone down well with both the opposition and his ANC party, thereby necessitating the current closed door talks to remove him from State House.
"So we leave this church well armed with the good blessings and prayer.so as the leadership of the ANC we have been well empowered as we move ahead. and we manage this transition", said Ramaphosa.
One case relates to 783 payments he allegedly received linked to an arms deal before he came to power.
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".
A senior ANC source told Reuters the meeting was scheduled to take place at 1200 GMT in Pretoria on Monday.
"He is not willing to step down voluntarily".
Ramaphosa also used the occasion to call on South Africans to reflect on the things that had gone wrong in the past and to make sure they do not happen again.
Then he referred to the topic that people really wanted to hear about - his confidential negotiations in recent days with Zuma over the president's exit after a scandal-marred tenure.
The ANC has insisted there will be no delay to the budget, which is on February 21.
Zuma initially refused to resign on Sunday night after being asked to step down by the top six officials.