Duma was speaking at the SACP provincial general council in Durban at the weekend.
Last month, Cosatu delegates refused to be addressed by ANC national chairperson Gwede Mantashe at the Cosatu national congress in Midrand.
Mantashe who was attempting to address Cosatu members on behalf of the ANC, was booed and heckled as unhappiness grows over the public servants’ wage talks.
At the same conference, SACP general secretary Solly Mapaila said that the ground was shifting and not in favour of the ANC and the SACP was ready to contest the 2024 elections.
Duma has discouraged public spats involving alliance leaders, saying an alliance summit was needed to improve communication and strengthen the tripartite alliance in the province.
“Public spats involving leaders, prolonged unnecessary tension, corridor gossiping and efforts to undermine each other as leaders and members should not be allowed to go unchallenged.
“The alliance was established to advance the objectives of the National Democratic Revolution,” Duma said.
He said the alliance was unique but each component has a distinct role and character "but together have the effect to complement one another and to make an impact".
“Transforming society, defeating poverty by ensuring access to economic opportunities remains fundamental.
“The majority of our people are poor and we need to be radical in terms of how we turn around the situation for the benefits of indigenous people, especially those in the townships and rural areas.”
He said deployed cadres of the ANC and alliance as a whole must work together and support one other in order to make an impact.
“We must maximise our strengthen instead of pulling against one another.”