Zuma is under growing pressure to step down in favour of his deputy and African National Congress (ANC) party leader Ramaphosa, with local media suggesting an exit deal is being hammered out.
Ramaphosa said in a statement he had "constructive" talks with Zuma.
He added that postponing the ruling ANC party's emergency talks "will enable President Zuma and myself to conclude our discussions and report back to our organisation and the country in the coming days".
"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.
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.
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