A 44-year-old man is still being questioned in Castlerea, Co Roscommon following the murder of Detective Garda Colm Horkan in the town on Wednesday night.
Det Horkan, who was from Co Mayo, died after he was shot a number of times with his own gun after it was taken from him following a struggle.
His funeral is to take place in his home town of Charlestown on Sunday.
Books of condolence have been opened at garda stations all over the country.
A vigil was also held in Det Horkan's memory in Castlerea last night.
A tribute was also paid to the detective by Garda Commissioner Drew Harris who said "a beloved member of the community" lost his life "for no good purpose" in "a random act".
In Charlestown, Co Mayo, parish priest Fr Tommy Johnston told RTÉ News he knew the family well and he has been with them.
Det Horkan was a reader at mass in his local parish of St James's, and is remembered there for his kindness and decency.
Dr Johnston said Det Horkan's father Marty told him he did not expect to have to bury his son before him.
Det Horkan was shot after he pulled over to speak to a man on the street.
Gardaí say he identified himself as a garda, but was attacked and shot several times with his own gun after it was taken from him.
All 15 bullets in the magazine were fired at him. He died at the scene.
The suspect who was arrested by two uniform gardaí a short time later remains in custody at Castlerea Garda Station for a second day today.
He can be questioned for up to three days.
The post-mortem examination has now been completed and Det Horkan's body is expected to be released to his family in Charlestown for burial in the next few days.
His State funeral will be subject to Covid-19 restrictions, but gardaí are examining in conjunction with the family a number of options by which members of the public and his garda colleagues can pay their respects in safety.
