Opposition members had sought judicial permission for lawmakers to cast secret ballots against the president's leadership. Jacob Zuma's alleged involvement in a series of corruption scandals has fueled widespread anger.
Chief Justice Mogoeng Mogoeng did not announce on Monday evening what date the Constitutional Court in Johannesburg would deliver the postponed verdict on whether or not secret ballots would be allowed in a no-confidence vote against President Jacob Zuma.
The date for the parliamentary vote also has yet to be scheduled.
The court's adjournment came after the opposition argued that only secret voting would enable representatives from Zuma's African National Congress (ANC) to cast ballots against the ANC leader and "vote with their conscience." The ANC currently holds a comfortable majority of parliamentary seats, and prior no-confidence motions against Zuma with open voting have fallen short.
A successful no-confidence vote would pave the way for Zuma's removal from office.
The speaker of the National Assembly, Baleka Mbete, a member of Zuma's ANC, previously had maintained that she did not possess the power needed to order a secret ballot in a parliament. Her argument caused an opposition party, the United Democratic Movement (UDM), to turn to the courts.
The date for the parliamentary vote at the National Assembly in Cape Town has not yet been scheduled
The president has been implicated in multiple corruption scandals, including misuse of taxpayer funds.
His March firing of Finance Minister Pravin Gordhan and ministerial reshuffling resulted in a downgrade of the country's credit rating and further inflamed public and political anger. The Democratic Alliance (DA), the primary opposition party, called for the no-confidence motion at the beginning of April.
Protests at the courthouse
Anti-Zuma protests have intensified in recent months, and Monday's court proceedings also drew South African citizens expressing vocal opposition to Zuma.
Hundreds of protestors gathered outside the Johannesburg courthouse as the bench listened to the opposition's argument. Mmusi Maimane, the leader of DA, addressed the sign-waving demonstrators, calling for ANC lawmakers to hold their party leader accountable for his actions.
"ANC members of parliament will have to choose between what is best for themselves and what is best for South Africa," Maimane said. "They did not swear [their oath of office] to be faithful to Jacob Zuma, or to the ANC ... They promised to be faithful to South Africa."
Supporters of various opposition parties - here the radical leftist Economic Freedom Fighters - have called for Zuma's removal
Recently, Zuma has also faced increased criticism from members of his own party, including from ANC Deputy President Cyril Ramaphosa.
Zuma has been accused of allowing the Gupta business family to influence government affairs by granting them lucrative state contracts and input into ministerial appointments.
The Constitutional Court found Zuma guilty of constitutional violation in 2016 after he used public funds for the renovation of his private home.
Zuma entered office in 2009. He is slated to step down as ANC leader this December and as president in advance of the next general election in 2019.
cmb/cmk (AFP, dpa)