The opposition call came as the ruling ANC's own integrity commission delivered Zuma a stinging rebuke over last week's cabinet reshuffle, saying it was "deeply perturbed" by the lack of consultation, according to local media.
The commission will reportedly once again call on the president to step down when he meets the party graft watchdog on April 9.
Zuma last week removed Pravin Gordhan from the top job at the treasury in a purge of cabinet critics that sent the rand currency tanking and triggered accusations that he was promoting graft.
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After holding emergency talks in Johannesburg on Monday, six opposition parties agreed to organise mass protests against Zuma as well as continuing to lobby for the vote of no confidence.
"Opposition parties are fully behind the motion of no confidence in Jacob Zuma," said Mmusi Maimane, leader of the the main opposition Democratic Alliance (DA).
The DA and the third largest opposition party, the leftist Economic Freedom Fighters Party (EFF), wrote to the national assembly speaker requesting an urgent sitting to debate the no-confidence motion. Parliament is currently in recess.
Speaker Baleka Mbete, who is also the chairwoman of the ANC, cut short an official trip to Bangladesh and returned home on Sunday to consider the opposition request.
"I am alive to the extreme challenges and sense of anxiety our young democracy is going through at this moment," Mbete said on Sunday.
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Zuma has survived several no-confidence votes in recent years.
"When other motions of no confidence failed, we were not facing the crisis that we are facing currently," said the president of the African Christian Democratic Party, Kenneth Meshoe.
"Now it is not only members of the opposition that acknowledge that we have a crisis, but members of the ruling party."
"This is not an academic exercise, we are serious about this," said Maimane. "We are working to remove Jacob Zuma."
With 249 seats, the ANC commands a strong majority in South Africa's 400-member parliament.
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For a no-confidence vote to pass, the opposition will require a simple majority -- meaning it will need to secure at least 50 votes from the ANC.
Zuma's sweeping cabinet overhaul exposed deep divisions within the ANC party and DA sources are confident that they can recruit enough support from ruling party MPs.
"There are quite a number of other colleagues and comrades who are unhappy about this situation, particularly the removal of the minister of finance who was serving the country with absolute distinction," said deputy president Cyril Ramaphosa said after the cabinet reshuffle.
