Save South Africa, a non-governmental group that has campaigned for Zuma's resignation because of corruption allegations, is expressing concern about negotiations between the president and deputy Cyril Ramaphosa, who said Wednesday that he anticipates a "speedy resolution" to the discussions about a transition of power.
Ramaphosa replaced the president as leader of the ruling African National Congress in December.
Steenhuisen said uncertainty was bad for the country and disruptive for the business of Parliament, where the Speaker this week took the extraordinary step of postponing the president's annual State of the Nation address to allow the ANC to settle its leadership battle.
He also assured the MPs that the talks would be concluded in a "day or two".
Mr Zuma, who spent time in prison for his part in the fight against apartheid, met the ANC's top six on Sunday.
Mr Zuma has repeatedly denied corruption allegations.
Zuma meanwhile was chairing routine cabinet committee meetings on Tuesday and not holding a "special cabinet meeting" as reported in local media, his spokesman said, as pressure mounted on the scandal-plagued leader to step down.
The Daily Vox team rounds up what three options Zuma faces in what could possibly be his last days as president.
If Zuma refuses a call by the executive committee to resign, it could organise a caucus meeting in parliament to discuss ways of removing the president, such as bringing a no-confidence motion or supporting one from the opposition.
"The president of the ANC has released a statement to say there is constructive engagement between (him) and Zuma", said Magashule.
South Africa had seen "systematic looting" under Mr Zuma's rule, and he "must go sooner rather than later", the foundation said. Ruling party leaders are uncomfortable with the idea of backing an opposition motion, fueling speculation that the ANC will make an internal decision to remove Zuma in the same way that President Thabo Mbeki was ousted in 2008 during his second term.
South African bonds were weaker on Thursday afternoon after the ANC could not provide further information on when President Jacob Zuma was set to resign as head of state. Zuma was due to deliver the address on Thursday.
Mashatile went on to say: "Where we are now, if the president does not want to resign voluntarily, we will recall him, like we did with President [Thabo] Mbeki".