SACP general secretary Blade Nzimande says although his party has called for President Jacob Zuma to resign, supporting anti-Zuma campaigns would be unadvisable.
Nzimande, who was speaking at the Cosatu's shop steward council in Joburg on Thursday, said the call for Zuma to step down was not easy.
The SACP took the decision last month following Zuma's sudden cabinet reshuffle.
They were later joined by another alliance partner, Cosatu who also called for Zuma's head.
Nzimande said the factional battles within the ANC and corruption within the government were matters of concern.
In what could be seen as a reference to the removal of former President Thabo Mbeki, Nzimande said the alliance back then dealt with "symptom but not the problem".
Blade Nzimande comments on Thabo Mbeki removal and factions within the ANC. Video: Zintle Mahlati
"You think you remove an individual and all the problems are solved. Yes removing an individual may be part of solving the problem.
"With President Mbeki, some of the issues was that there was not enough consultation. And now the same things are continuing. Which means what we haven't dealt with are factions which have captured the organisation, " said Nzimande.
Cosatu general secretary Bheki Ntshalintshali also took a veiled swipe at Zuma and advised that a leader listens when he is being told to step down.
"Don't ask reason why we are taking you out. There will be a time when you are elected and you must understand that your leadership is not required. Workers should not have to march for you and say step down. The time will come when they ask you to leave and you must be able to leave, said Ntshalintshali.
Ntshalintshali's comments may be seen as different from that of Cosatu president S'dumo Dlamini, who last week told Zuma to be "strong" at his 75th birthday bash in Soweto.
@ZintleMahlati