SDLP councillor for the area Peter Byrne told BBC Radio Ulster’s The Nolan Show the threats were “certainly an escalation”.
“We’ve had a number of threats around immigration policy in Newry to councillors on Newry, Mourne and Down over the last couple of months and it is deeply worrying. For me it’s a disgraceful attempt to intimidate local representatives who are ordinary people,” he said.
“I get that if people disagree with certain decisions of the council, but we live in a democracy, and if you agree with the strength of your argument, we should be able to debate it.”
He added that the threats are “absolutely deplorable”, and councillors have had to give their “home and work addresses to the PSNI”.
“The amount of misinformation being spread over the last couple of months that local council is somehow now responsible for immigration policy is absolutely ridiculous,” he added.
The PSNI said they were “contacting elected representatives to offer reassurance and crime prevention advice”.