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Speaking on RTÉ's Morning Ireland, spokesperson Martin Collins said if the row is not resolved, "it has the potential to escalate and it could even be worse next time, where potentially lives could be lost".
Baby John Collins, his 29-year-old mother Lynn Doyle and his 17-year-old uncle Mathew Collins were taken to hospitals after being shot at Parslickstown Green in Mulhuddard.
Their injuries are not believed to be life-threatening.
Mr Collins said he would encourage those involved "to see sense, come back to the table and to understand that violence and conflict is not inevitable, it is entirely preventable".
He said a garda presence is a really important deterrent as it would help to try to contain the situation and keep families apart.
He said there were "various attempts over the last number of months and indeed years to try and find a resolution through mediation", which have been unsuccessful.