A man continues to be questioned in connection with the murder of Detective Garda Colm Horkan.
The 49-year-old was shot dead with his own gun in Castlerea Co. Roscommon late on Wednesday night.
His gun was taken from him during a physical altercation with a man on the main street of the town.
Hundreds of people attended a vigil in Castlerea last night.
Garda commissioner Drew Harris led the tributes to Det Garda Horkan.
Speaking at Castlerea Garda Station before he visited the garda's family in Charlestown, Co Mayo, Mr Harris said he was a “beloved” individual, killed in a “random” act that had “no purpose”.
He said he was “a good garda out doing his duty” and that the killing was “an attack upon us all”.
Taoiseach Leo Varadkar also paid tribute to Det Garda Horkan, saying the whole country was grieving his death.
"Colm gave his life protecting the community he had served with distinction and courage," Mr Varadkar said.
"This tragedy is a heart-wrenching reminder of how much we owe our gardaí for the work they do all over our country. A nation is grieving.”