Crewe Town Council has carried a motion that "questions the reasonableness" of Crewe Alex's decision to not hold an inquiry into the Barry Bennell abuse.
The club last week announced that they would not fulfil a pledge made in 2016 to carry out their own investigation into their former Coach's crimes.
Last month the now 64-year-old was jailed for 30 years for 50 sexual offences against young boys.
The Town Council voted on the motion at a meeting last night and will now attempt to convince the club to change their minds again.
Council Leader Simon Yates told Silk 106.9: "I will be writing directly to the Chairman at the football club to ask them, as others have done, to reconsider their decision."
"Things like Hillsborough and Leveson show us how important it is, not just to bring about a conclusion in terms of criminal investigation, but for there to be a better understanding and a learning from what has gone on."
"This is not about attacking the club, this is about trying to get the club to understand that it has a bigger purpose here. It needs to respond to the damage that has been done to victims over the years."
Crewe and Nantwich MP Laura Smith is also calling for a wider, independent investigation.
Abuse survivors have called on Crewe Alex to apologise to them since Bennell was convicted last month.
The club's most recent statement on the matter states that a police investigation has already concluded they knew nothing about the abuse at the time of the offences:
"As the club has previously stated, this thorough investigation concluded that there was no evidence to corroborate that anyone at the club was aware of Mr Bennell’s offending. For the avoidance of doubt, this included both John Bowler and Dario Gradi as members of the club at the time."
"The club wishes to make it absolutely clear that it sincerely regrets the terrible crimes committed by Mr Bennell upon young footballers over a significant number of years. The club also wishes to reiterate its deepest sympathies to the victims and survivors of Barry Bennell."
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