Two men remain in custody in connection with the murder of Kenneth O’Brien whose dismembered remains were found dumped at a number of locations last month.
The men, one aged in his 30s and one his 50s, were arrested on Saturday and are being questioned at Naas and Leixlip Garda stations.
The arrests are the first in the investigation into the murder of the 33-year-old father-of-one.
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It is understood Mr O’Brien was shot dead and then dismembered with power tools.
Parts of his body were found in different locations.
Gardaí say a search operation to retrieve parts of the body which remain missing, believed to be parts of the hands, is still ongoing.
His torso was found by a passerby in a suitcase in the Grand Canal in Co Kildare last month and other parts of his body were found in the Grand Canal near Sallins, Co Kildare.
And parts of a power tool were recovered some distance away at the Royal Canal near Carton House, Maynooth, Co Kildare.
Mr O’Brien was reported missing on the evening of 15th January, and DNA analysis carried out on the body parts subsequently established that they belonged to him.
The motive behind the murder remains unclear.
Mr O'Brien was from Ballyfermot in west Dublin but had been living with his partner and child on Lealand Road, Clondalkin, west Dublin, since his return from Australia last month.
He had travelled to Australia to work while his partner and child remained in Dublin, and members of An Garda Síochána were recently sent to the country to establish further information on the time he spent there with a view to informing their investigations.
Investigating officers said they were following up some 300 leads shortly after they had established the identity of the victim following an appeal for information which prompted 100 calls from members of the public.
Mr O’Brien was described as a “loyal” and “intelligent” person during his funeral mass in Ballyfermot on Wednesday, and family members said there was some comfort to be found in the knowledge that he “died knowing he was loved and he loved us”.