Since Ramaphosa was elected as ANC President in December, pressure has been mounting on Zuma to resign due to his alleged involvement in a series of corruption scandals.
By A Correspondent| As reports flared that President Jacob Zuma might not get immunity, top ANC officials said Zuma's resignation letter could be received as early as next Monday.
"Cyril Ramaphosa has postponed the special NEC (national executive committee) meeting", the ANC said in a statement.
The Economic Freedom Fighters will request National Assembly Speaker Baleka Mbete to schedule an urgent sitting of Parliament on Tuesday, Democratic Alliance leader Mmusi Maimane said.
"We don't need to wear our boxing gloves because something fruitful and productive is happening between Zuma and Ramaphosa", said Mthembu.
Zuma has survived several no-confidence votes in parliament but faces another on February 22 filed by the far-left opposition party Economic Freedom Fighters.More news: We didn't play our number one game in final: Rahul Dravid
"He (Zuma) is not above the law, and must still face the 783 criminal charges illegally dropped over a decade ago and which the courts have now revived", said Maimane.
On a leaked audiotape, ANC treasurer general Paul Mashatile confirmed that Zuma had refused to resign and that the ANC had been ready to recall him at a crunch meeting. On Wednesday Ramaphosa said talks about a leadership transition were continuing and would be finalized in a matter of days, leaving the nation in political limbo.
The government also postponed an awards ceremony on Saturday at which Zuma was due to officiate, clearing the president's diary.
Ramaphosa and his backers say the process of removing Zuma should be allowed to run its course.
Despite the attacks on him, Zuma - a hardened political survivor - still enjoys some backing within the party, particularly among rural members and within his own Zulu community.
Save South Africa, an anti-Zuma campaign group, said it was "deeply concerned at the veil of secrecy surrounding negotiations" over the president's exit.