Cosatu was pivotal in Zuma's election as ANC leader at the party's elective conference in Polokwane in 2007.
Cosatu was criticised for his attendance after the trade union made calls for Zuma to step down in April.
Among those protesting against Zuma are members of several opposition parties, many civil-society groups, trade unions, business executives, the ruling party's alliance partners in the Communist Party, former President Mandela's granddaughter Ndileka, and even the 85-year-old Nobel Peace Prize victor, retired archbishop Desmond Tutu, who is in frail health. Cosatu's biggest affiliate, the National Union of Metalworkers SA (Numsa), was expelled in 2014 and general secretary Zwelinzima Vavi was axed the next year. Ntshalintshali said Cosatu no longer trusted and supported Zuma and wanted him to step down.
"We don't invite certain people and say we want so and so. This shall be communicated to the ANC, including engaging on its implications for our future alliance", said Ntshalintshali. "The issue of discomfort around the president attending - the ANC said it is them that shall decide who attends the May Day rally", Losi said.
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Police are searching an address in Moss Side which is separate to where the latest arrest was made. Investigations into Abedi's path to violent extremism were continuing apace.
The union announced on Tuesday that the decision had been taken during a meeting.
On whether Cosatu may have violated long-standing tradition in the alliance of internal communication mechanisms before alliance decisions are communicated to the public, Pamla dismissed that.
"We will continue to fight to have an alliance ..."
"We are not going to invite the president of the ANC to come and address the central committee". Their spokesperson, Alex Mashilo, said although the federation has not officially informed them on their decision, the SACP respected them for their independence.
The federation is also preparing for next week's policy review mini-congress.