The flags appeared close to new housing developments, as well as red, white and blue bunting at their entrances.
Mr Blair has said: “Everyone in our society deserves to feel safe, welcome, and respected in their communities, and to be able to live free from intimidation of any kind.
“It’s greatly disappointing to see the union flag be misused like this by some for the sectarian demarcation of territory. It’s unacceptable, and we must all take a firm and unequivocal stance against it.”
Ald. Boyle added: “Ballyclare is an overwhelmingly open and welcoming place, its population growingly diverse, with those from all sections of our community choosing to make it their home.
“It’s clear in just how many residents have contacted me opposing this kind of behaviour and expressing their concerns that this is happening, that those responsible speak solely for themselves.
“Our community doesn’t belong to any one group or identity – it belongs to everyone within it. Any action undertaken to suggest otherwise must be roundly condemned by all.”