On Saturday, members recommended endorsing Michael O'Malley instead.
The ward leaders will make a non-binding recommendation that will be voted on by the executive committee on Dec. 17.
McGinty has come under fire for his handling of high-profile cases, including the Tamir Rice investigation, which is currently under review by a grand jury to determine if the Cleveland police officers involved should face charges in the 12-year-old's shooting death. The Rice family has asked for an independent prosecutor to be appointed to the case.
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