The African National Congress (ANC) says it postponed its planned political alliance council because it wants the SACP and Cosatu to clarify their calls around the president first, before holding the gathering.
On Sunday, the SACP revealed that the ANC postponed the meeting at the last minute.
The communist party has voiced concern over the delay, saying its members had been looking forward to a robust debate.
The alliance council, comprising of national officials from the ANC, SACP, Cosatu and Sanco, would have met for the first time since the SACP and Cosatu called on President Jacob Zuma to step down.
The ANC's Zizi Kodwa says a decision was taken to first hold bilateral meetings with the alliance partners before the political alliance council.
“There are issues we may need to clarify before we come to the political council. The date is not set yet but it was important that in the interest of unity of the alliance, let us meet and clarify issues that have been raised by alliance partners, including for example what happened in Bloemfontein.”
In May, Cosatu took a decision to bar President Zuma from addressing its activities.
Their decision came after the president was booed and heckled during Cosatu's main May Day Rally in Bloemfontein and prevented from addressing workers.
Some unions affiliated to Cosatu objected to the president's address, saying by allowing him to address Cosatu's events a confusing message was sent about the federation's position on the president to step down.
Cosatu general secretary Bheki Ntshalintshali said they had taken a decision that allowing the president to address workers on May Day was inconsistent with its position for Zuma to step down.