Action SAs National Chairperson, Michael Beaumont, says they will not defend Johannesburg Mayor Dada Morero in a motion of no confidence.
The move is brought by the Democratic Alliance DA.
The DA is also targeting Chief Whip Sthembiso Zungu, while Al Jama-ah is pushing for the removal of Speaker Nobuhle Mthembu.
The council has 270 seats, with 18 political parties represented.
The African National Congress ANC is a leading party with 91 seats but falls short of the requisite 136 to govern.