Both President Zuma and I are aware that our people want and deserve closure.
Ramaphosa triumphed over Zuma's former wife, Nkosazana Dlamini Zuma, at last December's party elective conference.
South African President Jacob Zuma's exit from power because of scandals appeared to be getting closer on yesterday as his deputy, who is expected to replace him, said he anticipated a "speedy resolution" to transition talks he is holding with the president.
The ANC said they had been "fruitful and constructive discussions".
A "dominant view" emerged from the meeting, but it "wasn't the only view", ANC deputy secretary-general Jessie Duarte said at a media briefing. The party's national executive committee has been called to an urgent meeting on Wednesday to discuss Zuma's fate.
Parliamentary officials met Zuma to propose that the speech be postponed to establish "a much more conducive political atmosphere in parliament" and learned he was already writing to parliament to suggest the same thing, Mbete said.
"The fact that they cancelled Wednesday's ANC meeting probably means there is an agreement for him to go".
It is being seen as the first confirmation that Mr Zuma will step down shortly.
Party leader Mmusi Maimane said Zuma should be prosecuted for alleged corruption, amid speculation that the president might seek an immunity deal in exchange for his resignation.
In recent years his links to the wealthy India-born Gupta family, who are alleged to have influenced the government through their relationship with Mr Zuma, have caused his popularity to plummet. Zuma and the Guptas deny any wrongdoing, though the president paid back some money for the home upgrades after the Constitutional Court ruled against him.
Under Zuma's leadership, the economy has weakened and the ANC has performed poorly in elections, losing control of several major cities to the opposition Democratic Alliance. ANC credibility will be on the line if opposition parties are the ones to initiate the president's departure, and the leading political party will be concerned about its potential impact on the 2019 presidential elections.
However, Mr Zuma still has his supporters within the ANC - including at least two of the top six - so nothing is definite.