Ramaphosa was at Mandela's side, holding a microphone, when the leader addressed thousands outside Cape Town's city hall on the same day 28 years ago after his release. Zuma, whose presidency has been marked by numerous scandals, has stubbornly refused to budge.
The rand, which has tended to strengthen on signs that Zuma could step down before his second term as president ends next year, rose yesterday as investors increased bets that Ramaphosa would be able to unseat the embattled president.
He was addressing a crowd at the Grand Parade in Cape Town on Sunday, where the ANC held a rally to mark Nelson Mandela's centenary.
The beleaguered president faces a no-confidence motion in Parliament on 22 February.
With Zuma refusing a party request to resign, the African National Congress's top decision-making committee will meet on Monday. "We must keep our eyes on what is in the interests of all our people".
On Wedanesday, Ramaphosa confirmed that he had met with Zuma, saying their discussions were constructive and laid the basis for a speedy resolution to the leadership question in South Africa. It is Madiba's example that should inform our approach to the tasks that we must undertake.
Ramaphosa said it is the responsibility "of every leader who follows in the footsteps of Nelson Mandela to strive for the genuine unity of the ANC and for the unity of the South African people". Critics have expressed concern that Zuma may be requesting immunity from prosecution in exchange for his resignation.
"Our people want this matter finalised".
Ramaphosa, 65, was elected ANC president in December 2017 and is now most likely to become the country's next president.
She also cautions against "picking a fight with someone who is not fighting you".
"We remember the other Rivonia trialists - Walter Sisulu, Govan Mbeki, Ahmed Kathrada, Raymond Mhlaba, Elias Motsoaledi and Andrew Mlangeni - who were imprisoned alongside Madiba on Robben Island".
"Like Madiba, they were made to suffer for their convictions and, like him, their sacrifices, their courage and their indomitable spirit continue to inspire us"'.
"Allow (Ramaphosa) to lead, Leadership is a science, a profession and also an art".
Meanwhile, President Jacob Zuma and ANC president Cyril Ramaphosa will "conclude" their discussion on Zuma's exit as head of state within the next 48 hours, after which the outcome will be announced to the nation, News24 has reliably been told.