Conservative councillor David Meikle waved the Israeli flag as civic leaders raised the Palestinian flag over Glasgow's city chambers on Friday.
Jewish communities reacted angrily to the flying of the Palestinian flag saying it would stir up tensions.
Mr Meikle tweeted a picture of himself with the Israeli flag but his Twitter account has since been deleted.
Glasgow City Council said the flying of the Palestinian flag was to show solidarity with those affected by the conflict in Gaza.
Mr Meikle said the decision to fly the flag was taken without consulting council members and would do nothing to stop suffering on both sides of the conflict.
He is now being asked to resign his post as Councillor, simply for flying the Israeli flag.
Show your support for David Meikle by signing our petition.
The council is being two faced when they say this is about suffering on both sides. What they mean is they promote only anything to do with Palestine. If the council want Mr Meikle to resign then perhaps they should remove all councillers and replace them with a group of yes men who toe the party line and have no opinion.