Members of five Labour Party branches around Redcar and Cleveland have passed votes of no confidence in the party's council leader George Dunning, a letter seen by BBC News discloses.
Mr Dunning is criticised for "woefully inadequate political leadership" by the chair of the party's South Bank branch.
Labour recently lost overall control of the authority following the resignations of two councillors.
Mr Dunning said it was an internal matter and he would not be resigning.
A Labour North spokesman said it was the responsibility of the party's councillors to choose its officers.
Mr Dunning has been criticised for the authority's decision to sell a register office in Guisborough to a pub chain.
Campaigners had fought for the building to be turned into a community theatre, run by Earthbeat, a group made up of adults with learning disabilities.
The Guisborough Labour Party branch unanimously passed a vote of no confidence in Mr Dunning last month.
In her letter of 10 August, South Bank chairwoman Chris Foley McCormack, refers to the "adverse publicity" surrounding the register office issue and councillor resignations, and calls for Mr Dunning's resignation.
"This branch has no confidence that there is effective leadership in the group that will take the necessary action to put these matters right," Ms Foley McCormack writes to Eric Jackson, chair of the Labour group in the borough.
Ms Foley McCormack's letter states that similar motions have been passed by four other branches and "the Redcar Constituency Labour Party Executive".
Mr Dunning said: "There are proper laid down Labour Party procedures for dealing with these internal matters.
"On the question of my resignation I have already said publicly I have done nothing wrong and I will not be resigning."
A Labour North spokesman said it was "ultimately for Redcar and Cleveland's Labour councillors to choose their group's policies and officers".