The EFF says it has tabled a motion of no confidence against Tshwane Mayor Solly Msimanga.
Party leader Julius Malema said Msimanga was inconsistent and had not approached them through relevant channels regarding the removal of city manager Moeketsi Masola.
Malema was speaking at a media briefing in Johannesburg on Thursday.
Mosola was issued with a notice of intention to suspend him by the Tshwane Metropolitan Council on Wednesday.
The notice to suspend him comes after Mosola was recently implicated in the awarding of an alleged irregular tender to engineering consultants GladAfrica, worth a reported R12bn.
Mosola - who has denied the allegations, insisting that all processes were above board - was given seven days to make written submissions on why he should not be suspended, after prima facie evidence emerged in his submissions that he unlawfully concluded a contract.
"We are not supporting the Tshwane city manager and we think that there is inconsistency because Solly sat next to the city manager and announced that there was nothing wrong. And now, if there is something wrong, they must both take responsibility," Malema said.
City manager 'being used as scapegoat'
He added that the mayor's claim that he was unaware of the contract in question could not be accepted, because Mosola had emailed a DA member about the contract and copied the mayor.
"Solly says he didn’t know about this corruption they are talking about, but the city manager wrote a letter, which we have a copy of, to one of the DA members who was investigating this," Malema said.
He added that Msimanga was using the city manager as a scapegoat and that the EFF would not allow that.
The EFF knew that the city manager was being punished because it was suspected that he was the one to expose the fact that Msimanga had hired former Tshwane chief of staff Marietha Aucamp.
Aucamp resigned in May after it was revealed that she did not have the proper qualifications for the job.
"The reality of the situation is that Marietha was touched, and she was supposed to be an untouchable person. Solly sat in a panel which interviewed Marietha and appointed [her] without qualification."
Malema said the EFF hoped other political parties, including the DA, would support them in their new motion to oust Msimanga.
'We don’t owe DA our votes'
Msimanga has emerged as the DA’s choice to drive the 2019 election campaign as its Gauteng premier candidate.
In response to this, Malema said the EFF would only offer its support to any "credible candidate" when it came to premiership candidacy of the province.
"If the ANC has a credible candidate, let them put the candidate forward. If the DA has another credible candidate, who is not Solly Msimanga, they can put that person forward. We will support that person," he said.
Malema added the EFF would not engage in any behind-the-scenes meetings with political parties.
"We don’t want to be engaged in secret meetings, where we are going to be accused of tenders and all those things… If it means voting for an ANC candidate, we will do so. We don’t owe DA our votes."
He added that, if the ANC and DA did not bring any "legitimate and credible" candidate forward, the EFF would not vote.