A motion has been passed by Mayo County Council calling on staff to stop cooperating with the Department of Integration when it comes to housing asylum seekers.
Councillors want an "agreed strategy" put in place on the housing of international protection applicants.
Amongst their requests are that contracts yet to be taken up are paused.
Fine Gael Councillor Peter Flynn said they want the Government to listen.
Mr Flynn told Newstalk: "We don't know what the implications are, but it certainly will make the job of government that bit more difficult when it comes to Mayo.
"I would hope that it's not just Mayo that the Government looks at, it's the entire country. To figure out, how do we do this best?
"The last thing we need as a country is social discord amongst our people, be they residents or be they refugees into our country."
Mr Flynn added: "Migration has played a huge role in the success of Ireland over the last 20 years. No one is doubting that, and we want to continue to see that in the future. But we don't want to see a situation where residents are going to start pointing fingers at refugees because our tourism industry is starting to suffer, or because our critical services begin to fail.
"We're getting close to the brink of that, and we really want to avoid that."
The motion comes after a protest earlier this month in Ballinrobe, Co Mayo, outside a former hotel that was earmarked to accommodate 50 international protection applicants.
It was stood down after the Department of Integration said it would be used to house families and children.
