Shortly before midnight, the SABC state broadcaster said Zuma had been told in person by Ramaphosa that he had 48 hours to resign.
"Should he refusal, we would have to resort to a parliamentary process, with a 62 per cent majority, with the support of other opposition parties, we are certain it will pass", Mr Gigaba said.
Mr. Zuma has been ordered to resign by the ruling ANC party, and is expected to respond to the order later in the day.
He says he will make a statement later.
In a briefing to South African state television on Wednesday, Zuma said he was confused about why he was recalled by the ANC. The party earlier issued a statement‚ saying it had abandoned its bid to take the matter to court as it had come to an understanding with the ruling party. He has emerged unscathed in a slew of no-confidence votes over the years despite the extraordinary number of corruption allegations against him, counting on the ANC's dominance in parliament to shield him. "What is this hurry?"
However, resistance to Mbete's plan is not likely.
The announcement by the African National Congress did not immediately end the protracted turmoil in a party that was the main movement against white minority rule and has led South Africa since apartheid ended in 1994.
Mashatile said that the ANC would push for the tabling of a motion of no confidence in Zuma, to be debated in parliament as early as Thursday.
Government leaders hope the standoff can be resolved ahead of the unveiling of the national budget in parliament on February 21, which would go some way toward reassuring investors that the country is getting back on track.More news: The Redmi Note 5 Pro's dual-camera bump looks very familiar
Mr Zuma's grip on power began to erode when Cyril Ramaphosa narrowly won the ANC's elective conference in December and was chosen to become the party's new president.
Zuma was elected president in 2009.
Members of the wealthy family, who own several businesses in the country, are increasing their fortune through relationship with President Zuma.
Police said three unidentified people had been arrested in investigations into "Vrede Farm" - allegations that millions of dollars of public money meant for poor dairy farmers was syphoned off by the Guptas.
A judicial commission is about to start a probe of those allegations.