Zuma has been at loggerheads with Finance Minister Pravin Gordhan for months, and this week abruptly ordered him to return home from a foreign investment trip as speculation rose of a dramatic political showdown.
Gordhan is supported by several senior ministers and many international investors, as well as being widely admired by ordinary South Africans and veterans of the anti-apartheid struggle.
He has campaigned for controlled spending and against corruption, but Zuma's allies have accused him of thwarting the president's desire to enact "radical economic transformation" tackling racial inequality.
"We recorded our objection to the intended reshuffle."
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Zuma met with the SACP, which is a junior coalition partner of the dominant ANC, on Monday.
Gordhan's fate has become a battleground over the future of the ANC, which Nelson Mandela led in the fight against apartheid and when it won the country's first democratic elections in 1994.
Zuma is due to step down as head of the party in December, ahead of the 2019 general election.
"The battle for control of the ANC will... Culminate in the defeat of Cyril Ramaphosa, Gordhan and their faction at the December conference," the Eurasia consultancy predicted in a briefing note.
"This group is then very likely to split off from the ANC in a possible major realignment of South African politics."
Zuma's planned sacking of Gordhan may have been put on hold due to the death of celebrated anti-apartheid activist Ahmed Kathrada, 87, on Tuesday.
Kathrada was a fierce critic of Zuma, and his funeral on Wednesday became something of a rally against the president, who did not attend at the request of the family.
In December 2015, Zuma unexpectedly sacked finance minister Nhlanhla Nene and replaced him with a little-known lawmaker, triggering panic among investors and a sharp drop in the rand.
Just four days later, Gordhan was appointed to the role to calm the markets.
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