Earlier this month, President Zuma was booed at a Cosatu May Day rally in Bloemfontein.
Johannesburg South Africa's ruling African National Congress denied reports that President Zuma's removal would be discussed at a key party meeting this weekend.
Three Cosatu affiliates had sent a request a week before the rally to barre Zuma from addressing members of the union on Labour day.
The federation has been vocal in its criticism of Zuma as leader of the country.
Cosatu are committed to their alliance with the ANC and the South African Communist Party (SACP), and they will work towards uniting the alliance, said Ntshalintshali.
ANC spokesperson Zizi Kodwa says while it's the party's responsibility to deploy leaders, Cosatu can invite specific leaders.
The union has taken a decision to bar President Jacob Zuma from addressing its activities.
The Special Central Executive Committee (SCEC) of Cosatu met on Monday to analyse the National May Day Celebrations held on May 1, amongst other topics.
The parties believe that without fear of retaliation from the ANC - which would be afforded buy a secret ballot - numerous ruling parties' MPs would vote in support of getting president Zuma out. Cosatu reiterated its commitment to the tripartite alliance though.
"We are not going to invite the president of the ANC to come and address the central committee".
Ntshalintshali said: "One of the unmentioned reasons for the disinvestment of GMSA [GM South Africa] is the question of lack of leadership, which has been raised by rating agencies".
The ANC, however, said it had not been informed of the federation's decision not to allow Zuma to address its gatherings and would respond in due course.