Ramaphosa is due to give a speech tomorrow as part of year-long celebrations to mark 100 years since the birth of Mandela.
Zuma has not said whether he will resign voluntarily before his second term as president ends in the middle of next year.
"Because our people want this matter to be finalized, the national executive committee will be doing precisely that", he said. He also promised to tackle corruption.
The ANC's chairperson said on Saturday that South Africans should be patient with Ramaphosa as he holds talks with Zuma for a transition of power. "While preserving the value of money is our main mandate, our goal is to be a bastion of institutional strength, contributing to a stable and prosperous economy that serves the well-being of all South Africans, and guided in part by Madiba's values", said Lesetja Kganyago, South African Reserve Bank Governor. A senior ANC source told Reuters, however, that the committee was likely to discuss Zuma's situation at the meeting.
Ziyanda Peter, a 33-year-old unemployed mother of four from Langa township in Cape Town, is looking to Ramaphosa to rebuild the ANC and revive the hope that South Africans had for a better future when Mandela led the country.
Many former supporters of the president want him to resign because of his links to scandals that have sapped support for the ruling party and hurt one of Africa's biggest economies, but there is a growing sense of unease over the lack of information about the confidential talks between Zuma and Ramaphosa, his expected successor.
He said Ramaphosa had returned Gauteng province, where the ANC's headquarters is located in the country's commercial capital Johannesburg.
Ramaphosa also used the occasion to praise the Congress of South African Unions (Cosatu) for the role it played in ensuring that the minimum wage is finalised and implemented this year from May 1.
On Sunday, Ramaphosa shone on stage under a warm Cape Town summer's day, however, all eyes will now be on the ANC NEC which meets on Monday to finalise Zuma's exit.
The Sunday Times has learnt that Ramaphosa is trying to secure Zuma's co-operation in the state-capture investigations and has solicited opinions on legal avenues that would allow the president to avoid prosecution or receive a reduced sentence. "But if needs be, it is an ideal for which I am prepared to die", said Mandela, who died in 2013 at the age of 95.
Since Zuma was replaced as head of the ruling party in December, the ANC has turned against him, and a looming no-confidence vote scheduled for February 22 may succeed, if the ANC leadership doesn't convince him to step down first.