The list included libraries, community centres, football pitches and golf and bowls centres across the city.
Glasgow Life lost more than £40m in the last year as a result of closures due to lockdown.
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Glasgow City Council agreed to underwrite a £100million income guarantee for Glasgow Life allowing it to open around 90 venues but that meant still almost 80 would remain closed.
Mr Graham, who was chair of Glasgow Life when Labour were in control at the council, said in the motion: “All 171 Glasgow Life venues should re-open as soon as it is safe to do so, subject to sufficient funding from the Scottish Government.”