This weekend, opponents proposed a motion of no confidence against Zuma at a meeting of leaders of the African National Congress party, which has led South Africa since the end of white minority rule in 1994.
Many in the party attribute the ANC's poor performance in local elections last year to scandals surrounding the president and want to shore up their popularity ahead of national elections in 2019.
State broadcaster SABC said the chairman of the National Executive Committee meeting did not allow debate on the motion because it was not on the agenda, though the meeting was continuing late today.
Zuma survived a similar move to oust him at a committee meeting in November, but unease within the ruling party grew after he fired Pravin Gordhan, the widely respected finance minister, in a Cabinet reshuffle in March.
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Zuma's ties to the Gupta family, Indian immigrant businessmen accused of trying to manipulate top government leaders for financial gain, has also stirred public anger.
This weekend's edition of the Sunday Times reported on emails allegedly showing the Guptas' control over some Cabinet ministers and state-owned companies, as well as the involvement of Zuma's son Duduzane, a Gupta associate. The Guptas deny any wrongdoing.
In another scandal, Zuma was forced to reimburse some state money after the Constitutional Court ruled against him last year in a dispute over millions of dollars spent on his private home.