The president appeared to have headed off the most serious threat to his hold on power since he came to office in 2009.
Zuma has been weakened by a series of scandals but the manoeuvre to oust him took many by surprise in the African National Congress, which has held power since 1994.
A weekend meeting of the party's executive was extended into Monday after a rebellion led by senior government figures, including at least four ministers.
Local media said the meeting, which ended late on Monday evening, was tense, with tempers flaring and some ministers threatening to resign if Zuma stayed.
But the president appeared to have headed off the most serious threat to his hold on power since he came to office in 2009.
He left South Africa early on Tuesday to attend the funeral of Cuban leader Fidel Castro.
The ANC announced it would hold a press conference at 2:00 pm (1200 GMT) on the meeting's outcome.
"The president told us that he will never step down, as it would be like handing himself over to the enemy, and that there are people who want to see him in jail," an unnamed source at the closed-door meeting told the News24 website.
It said Zuma's loyalists had rallied strongly to his defence during Monday's sessions.
The president has been hit by multiple corruption allegations and damaging court rulings this year, while the ANC suffered a serious setback in local polls in August and unemployment has hit a 13-year high.
Zuma has been under renewed pressure since a corruption probe earlier this month unearthed fresh allegations of misconduct.
The probe by the country's top watchdog uncovered evidence of possible criminal activity in his relationship with the Guptas, a business family accused of wielding undue political influence.
However Zuma, 74, retains strong loyalty among many rank-and-file ANC party members, as well as its lawmakers.
He easily survived a vote of no confidence in parliament on November 10.