Councillor Claire Darke said council leader Ian Brookfield should consider his position following a botched attempt to oust Councillor Celia Hibbert at a meeting last month.
Mr Brookfield says he has the full support of the "overwhelming majority" of the city's Labour group.
It comes after the Labour group voted to suspend Councillor Hibbert indefinitely for defying the party whip in a key vote.
Following an appeal her suspension was quashed by regional party bosses, who restored the party whip after ruling the penalty was too harsh.
Former Mayor Mrs Darke is understood to be heading up a small band of disgruntled Labour group members intent on removing Mr Brookfield as leader.
In a letter to all Labour councillors and the authority's governance director David Pattison, she claimed that group members were "misled" ahead of the vote to suspend Councillor Hibbert.
The Park ward councillor accused Mr Brookfield and the executive team of knowing there was "no evidence" against Councillor Hibbert and of withholding information from the Labour group.
Councillor Darke added: "Consequently leader, it seems right that you should consider your position and stand down, at least temporarily pending an independent enquiry into your actions, together with the concerns that the culture of Labour councillors bullying and harassing one another continues, with it seems, the active support of the leader.
"I shall be sharing my concerns with the regional director and National Executive."
Other councillors who are understood to have backed Councillor Hibbert in the vote include Rupinderjit Kaur (Spring Vale), Sandra Samuels and Zee Russell (both Ettingshall), Lynne Moran (St Peter's) and Rashpal Kaur (Bilston East).
Mr Brookfield defended his actions and maintained that he had the support of the majority of the Labour group on Wolverhampton Council.
He said: "As in any walk of life, in any large grouping of people, be that football clubs, social clubs or workplaces, you will always find one or two disgruntled or disaffected people, and the comments made should be taken in that regard.
"I have the full support of the overwhelming majority of the Labour group in Wolverhampton."
The row started after Councillor Hibbert breached Labour group rules by abstaining in a vote on a senior leadership review.
An appeal ruled against allegations she had encouraged others to do the same, while claims she had attempted to join the Tories were denied by Conservative group leader Wendy Thompson.
Regional bosses ruled that Councillor Hibbert be handed a written warning for her conduct. She was also ordered to attend training on "the role of the whip and its purpose".