On Sunday, the ANC marked the commemoration of Mandela from prison in Cape Town.
"This year we are called upon, all of us, to look at where we have come from and to look at our weaknesses, to look at the challenges we face", Ramaphosa said.
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.
In a strongly worded statement the ANC in the Sarah Baartman Region says the sooner Jacob Zuma steps down from the Presidency the better, labelling his efforts to hold on to the position as "unprincipled conduct".
Ramaphosa, one of the richest black South Africans, has had a hard relationship with Zuma since he left his business career and returned to full-time politics five years ago, and became deputy president in 2014.
Zuma's spokesman did not respond to calls seeking comment.
But Zuma's wife Tobeka Madiba-Zuma caused a stir on social media on Friday after she posted a picture on her Instagram account, @firstladytzuma, showing her and the president inside what appears to be a plane, with part of the caption reading "It's going to be ugly".
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)".More news: Mixed reviews on LLBean's new return policy
Unlike Zuma, Ramaphosa was not driven into exile for opposing apartheid, which some of the party's more hardline members hold against him.
When Mandela finished, Ramaphosa briefly addressed the crowd.
"The REC would like to appeal to the NEC members to speak in unison on this matter and manage contradictory statements that cause confusion in the rank and file and society at large."The more the matter is prolonged, the more the people of South Africa are losing hope in the ANC and opportunistic elements occupy the space, exclusively to topple the ANC from power".
Jailed for 27 years, the anti-apartheid leader addressed an ecstatic crowd from the balcony of Cape Town's City Hall on February 11, 1990 and was elected as South Africa's first black president four years later.
Zuma had been due to officiate at a diplomatic awards ceremony in Cape Town on Saturday, according to his office, but that event has been postponed.
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.
Speaking at the Mandela celebration on Sunday, Cosatu second deputy-president: Zingiswa Losi said Zuma had to be recalled in the interest of the country.