Mr Blair was speaking after the memorial, dedicated to the three victims of an IRA attack, was targeted for the 19th time when slogans were painted over it and two wreaths removed.
Councillor John Blair said: “This unwanted vandalism must stop. The friends and families of the victims deserve to be able to remember their loved ones without fear of intimidation.
“Those behind this thuggish behaviour must be stopped and I would urge anyone with information to contact the PSNI as soon as possible.
“But this hasn’t been the only scene of vandalism in recent days, with a spate of republican graffiti discovered across Glengormley last night – including at the site of the former PSNI station on the Antrim Road.
“While these acts continue to offend the local community, their spirit will not allow this mindless vandalism to hinder good relations in the area.”