On Monday, Maimane’s spokesperson, Graham Charters, said the party was not going to make any efforts to mediate between Maimane and the EFF's leader, Julius Malema.
“If the EFF has an issue with the DA leader, then they must do so in the appropriate forum, not on the pages of newspapers. It is not Maimane’s job to do so,” he said.
Last week, Malema warned the DA that if it did not remove Zille, his party would remove the DA from power in the three metros it currently controls.
He said the EFF did not owe anything to anyone, and if the matter escalated to a point where fresh council elections would need to be called in metros where the DA was in power, “we will fold our hands and watch”.
But Maimane said the DA was a party of “due process” and that it would await the outcome of a disciplinary hearing before a decision on any further action was taken.
Zille was suspended from party activities over her tweets in defence of what she called positive aspects of colonialism.
“If the EFF are happy to 'fold their arms' and abstain from voting, then the people of South Africa must know that it was the EFF who handed power back to the corrupt, Gupta-controlled ANC."
“Malema himself has said things in public that I do not agree with, that threaten the project of reconciliation in South Africa. Nevertheless, we are working together in the interests of South Africa,” Maimane had said.
EFF secretary-general Godrich Gardee said the DA's refusal to fire Zille meant there was no difference between the party and the ANC, which “chooses Zuma over the country”.
“The ANC is also conducting its business according to its own constitution. If we say the ANC should never choose Zuma over the country, the same should apply to the DA."
“We have no contractual engagement with the DA, we are not in coalition and we are not friends. We just voted with them and can stop any time."
He added that the party could not be blamed if power goes back to the ANC as they continued to play their role as opposition. “The voters know who they voted for,” Gardee said.