The ANC's 88-strong national executive committee (NEC) had agreed to meet in Cape Town to discuss Mr Zuma's refusal last weekend to voluntarily step down as South Africa's president, and had been expected to recall him from office. There has been media reports that Zuma will resign or his party will force him to do that.
Mr Ramaphosa said that postponing a meeting on Wednesday of top ANC officials would "enable President Zuma and myself to conclude our discussions.in the coming days".
Zuma and Ramaphosa were seen taking part in cabinet committee meetings, according to pictures circulated by the official South African government account on Twitter.
"The discussions were constructive and lay the basis for a speedy resolution of the matter in the interests of the country and the people", Ramaphosa said.
The meeting between Zuma and Ramaphosa took place after Speaker of the National Assembly Baleka Mbete announced the postponement of the state of the nation address, which Zuma would have delivered on Thursday.
The delay increased speculation that a deal for Zuma to resign had been ironed out.
Ramaphosa said despite this, the work of government and parliament is continuing.
Zuma's second five-year term is scheduled to end with elections in 2019, but many ruling party members want Ramaphosa to take over as soon as possible so that the party can try to recover the trust of voters alienated by the president's scandals.
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In previous years, opposition lawmakers have shouted Mr Zuma down and been ejected from parliament by security guards in chaotic scenes.
The secretary-general would not say who would deliver the state of the nation address once a new date is announced.
Independent political analyst Ralph Mathekga told AFP that Mr Zuma's departure had been mishandled by the ANC.
"The fact that they cancelled Wednesday's ANC meeting probably means there is an agreement for him to go".
The ANC was the main anti-apartheid movement for decades and has led South Africa since the end of white minority rule in 1994, but its moral stature has diminished because of concerns about Zuma and wider problems of corruption and mismanagement.
Zuma's presidency has been dominated by an economic slowdown, record unemployment and allegations of corruption.
He faces several court cases, including action relating to 783 payments he received allegedly linked to an arms deal before he came to power in 2009.
He is still fighting almost 800 counts of corruption over an arms deal from the late 1990s and his ties with the Gupta brothers, a family of wealthy Indian-born businessmen, are the subject of a judicial inquiry on grand-level corruption.
Mr Ramaphosa, who promised to fight corruption when campaigning to be the ANC's next leader, will be its candidate in South Africa's presidential election.