On the discussions about the transition of power from President Jacob Zuma, Ramaphosa said it was important that they be managed with care and goal, and that the interests of South Africans were put first.
The 75-year-old Zuma, in power since 2009 and mired in corruption allegations, has been living on borrowed time since Ramaphosa took over his other role as leader of the ruling party in December.
"Our people want this matter finalized", Ramaphosa told a crowd of about 3,000 people on the Grand Parade next to the Cape Town city hall on Sunday to commemorate the 28th anniversary of Nelson Mandela's release from prison.
He added: "We know you want this matter to be finalised".
The leader of South Africa's ruling party has acknowledged growing impatience over the failure to resolve President Jacob Zuma's future.
In his speech, the deputy president said the government will wage a "relentless war against corruption and mismanagement of the resources of our country" and that the justice system will punish the guilty.
Zuma's spokesman did not respond to calls seeking comment.
Taking to Instagram, Madiba-Zuma posted a picture of her and the president and captioned it "my everyday crush".
Local media said a key sticking point in the negotiations was the potentially huge legal fees Zuma is facing from prolonged court battles against multiple criminal cases.
First Lady Madiba-Zuma, however, who clearly supports her husband's stance to remain in power until next year will have none of these antics to remove her from the stately home as well and cautioned against "picking a fight with someone who is not fighting you". "He will finish what he started because he does not take orders beyond the Atlantic Ocean #mattersofthestomach (sic)".
Ramaphosa said they would draw on Nelson Mandela's wisdom.
When Ramaphosa sold off his business in 2014 and returned to politics, he became one of South Africa's 20 richest people.
The rally was part of ANC celebrations marking 100 years since Mandela's birth - as well as efforts by Ramaphosa to try to revive the party's tainted reputation ahead of next year's general election.
Yesterday, News24 reported that five of the top six in the ANC had pulled out of all mass mobilisation events that were planned for Cape Town because officials had been summoned to Gauteng for urgent matters.
Zuma has not spoken since being asked to resign by senior ANC officials on February 4.
Zuma, who no longer holds a top position in the party, has not said whether he will resign voluntarily before his second term as president ends in the middle of next year.
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