Late South African Communist Party leader Chris Hani was assassinated 25 years ago on April 10 1993.
"The newly elected NEC won't fail South Africans, because they know what's at stake," a Cosatu spokesperson said.
The SACP says anyone found guilty in the state capture inquiry will be dealt with, but all sides must be heard.
Former ANC member of Parliament Vytjie Mentor said, while the decision caught her by surprise, she was concerned that Zuma was not explicit that the commission’s terms of reference will be
"It is very important the announcement made by Zuma must be clarified as a matter of urgency."
Blade Nzimande says he is not concerned that he was not elected to the ANC's NEC.
The alliance partner has lambasted Zuma's appeal, saying "deeply concerned South Africans" want Zuma to comply with the judgment.
SACP spokesperson Alex Mashilo says that the war against President Jacob Zuma is not over and they will still be on the trail of having him recalled.
“We hope that this conference will become successful and stop the wars that Zuma declared against the alliance."
The SACP, in a historic move, contested the by-elections in the municipality's 21 wards on November 29.