Campaigners are set to urge council chief executive Sue Bruce to ask the Scottish Government to keep prison visiting committees at Saughton and Addiewell.
Councillor Joanna Mowat will raise a motion on Thursday on behalf of city residents who want to keep the practice of citizens examining conditions at jails.
Justice Secretary Kenny MacAskill said a consultation on the issue failed to find “decisive evidence” to keep the system and wants them to be replaced them with an independent advocacy service for prisoners.
The move has been met with significant opposition.
Councillor Mowat is to table a motion that the council “regrets this decision and will seek to join with others to campaign to retain independent monitoring of Scottish penal institutions”.