On Monday, the body of a man in his 20s was found in a bedroom of a property at Assolas, Kanturk, in north-east Co Cork.
The bodies of another man in his 20s and a man in his 50s were later found on adjoining land.
The men have been named locally as brothers Diarmuid and Mark O’Sullivan and father Tadgh.
Garda Superintendent Adrian Gamble confirmed all three were from one family, and all had suffered gunshot wounds.
It is understood that the shootings are related to a dispute over a will and the future inheritance of a 150-acre farm that had been simmering recently, according to the Irish Times.
Detectives believe that one of the sons and his mother returned to the family home after some time away on Sunday night and that this man was later shot in his bedroom.
The woman managed to flee the house and went to a neighbour to raise the alarm.
Preliminary indications show that both men had suffered tragic gunshot wounds. I confirm that all three deceased men were from the one family.
Mr Gamble said gardaí had been alerted to a “critical firearms incident” at around 6.30am on Monday.
He added: “A short time earlier, a female in her 60s alerted neighbours that a firearm had been discharged at her home.
“Gardaí were then informed that three males were present in the house, and that one may have suffered gunshot wounds.
“Throughout the course of the morning and early afternoon, Garda negotiators attempted to make contact with people that may have been in the house.”
Gardaí knew the family had three licensed firearms at the house – two rifles and one double barrel shotgun – so they did not attempt to enter the property.
“Shortly after 1pm, members of the emergency response unit approached the house and sadly, the body of a male in his 20s, with a gunshot wound was discovered in a bedroom. No other people were present,” Mr Gamble said.
Outhouses beside the farmhouse were then searched and the Garda Air Support Unit was deployed as well as the North Cork Divisional Search Team, who began searching fields around the farm.
The Air Support Unit spotted two bodies at about 1.45pm in fields near the property and found the bodies of the father and other son, who appeared to have suffered gunshot wounds, and two firearms.
Mr Gamble said: “Preliminary indications show that both men had suffered tragic gunshot wounds. I confirm that all three deceased men were from the one family.”
Local representatives said the tragedy had left the community “numb.”
“It has come as a real shock to the community. We’re a very close knit community here and to be honest with you, every one is just numb.”
Fine Gael councillor John Paul O’Shea said: “Everyone is deeply saddened and shocked by this tragedy.
“My thoughts go out to the family and the wider community of Castlemagner and Kanturk as they come to terms with this unimaginable loss.
“There is a strong and determined community spirit in Castlemagner and the community there I know will rally around their families, neighbours and friends in the coming days as they deal with this tragic loss.”
Gardaí indicated on Monday that they are not looking for anyone else in relation to the incident.
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A full investigation has been launched, and the state pathologist and the Garda Technical Bureau are to visit both scenes.
A Garda spokesman said: “An Garda Síochána is not looking for any other persons in connection with this incident at this time.”
However, an appeal has been made for witnesses or information, with anyone who may be able to assist asked to contact investigating gardaí at Mallow Garda Station on 022 31450, the Garda Confidential Line on 1800 666 111 or any Garda station.