Taoiseach Leo Varadkar has said that Detective Garda Colm Horkan gave his life protecting the community he served.
Mr Horkan was shot dead while on duty in Castlerea in Co Roscommon on Wednesday night.
A man aged in his 40s has been arrested and is being held at Castlerea Garda Station.
Paying tribute to the detective, Mr Varadkar said: “Last night we lost a member of An Garda Siochana in the most tragic of circumstances and today a nation is grieving.
“I’ve spoken to the Garda Commissioner today and the Minister for Justice and we are in touch with the family of Detective Garda Colm Horkan to offer our condolences and support.
Our gardai are our guardians of the peace and defenders of the rule of law and they are role models in our society.Leo Varadkar
“I extend it also to all of his colleagues in Castlerea Garda Station, to every member of An Garda Siochana, his friends and all who knew him.
“Colm gave his life protecting the community he served with distinction and courage during his 24 years as a member of An Garda Siochana.
“His story is the same as the thousands of men and women who wear the uniform – a story of courage, sacrifice and service.”
Speaking on the steps of Government Buildings in Dublin, Mr Varadkar added: “Our gardai are our guardians of the peace and defenders of the rule of law and they are role models in our society.
“This tragedy is a heart-wrenching reminder of how much we owe our gardai for the work that they do all over the country.
“They protect and serve our citizens, our communities and our country, every day putting themselves in the frontline of crime prevention on behalf of all of us.”
Irish President Michael D Higgins said the detective’s death has been a shock to everyone.
He added: “As President of Ireland I wish to express my deepest sympathy to the family and friends of the garda, and to all those who have been affected by this tragedy.
“An Garda Siochana play a crucial role in our communities and this loss of life is traumatic for our society as a whole.”
President of the Garda Representative Association Jim Mulligan said: “On behalf of the GRA, I extend our deepest sympathy to the family of our colleague fatally shot in the line of duty in Castlerea, Co Roscommon, overnight.
“Our brave colleague died as result of injuries sustained when he was responding to an incident. He was based in Ballaghaderreen, Co Roscommon, in the Castlerea District,” he said.
North of the border, Police Service of Northern Ireland Chief Constable Simon Byrne offered his condolences.
“Awful news this morning coming from @GardaTraffic with the death of a Garda colleague in Castlerea,” he tweeted.
“Thoughts from all @PoliceServiceNI with his family, friends and colleagues at such a difficult time.”
In 1980, two members of the Garda were shot dead near Castlerea in the village of Loughglynn.
Detective Garda John Morley and Garda Henry Byrne were killed by armed bank robbers.
Roscommon-Galway TD Denis Naughten said the community is in shock following the latest incident.
“We are absolutely devastated, shocked and saddened by what we heard overnight,” he told the PA news agency.
“A member of An Garda Siochana doing his job protecting the community has lost his life in such very tragic circumstances.
“This is devastating news for his family and the gardai in the Castlerea district and for the local community, and our thoughts and prayers are with Colm’s family at this time.”
Fianna Fail justice spokesman Jim O’Callaghan condemned the shooting.
Shocked and saddened at the killing of a member of An Garda Siochana in Castlerea. Our thoughts and prayers are with his family, his community and all his colleagues who continue to bravely protect us all from harm every day.— MicheÃ¡l Martin (@MichealMartinTD) June 18, 2020
“The brutal killing of a member of An Garda Siochana in the line of duty is appalling,” he said.
“The garda detective was shot dead while working to keep his community safe.
“I want to express my sadness at the loss of a garda serving in the line of duty. It reminds us that members of An Garda Siochana display courage and bravery every day in their work in communities across Ireland.
“This was not just an attack on one individual, it was an attack on civilised society. We need to send out the message loud and clear that we will simply not tolerate this brutal brand of criminality against members of An Garda Siochana.”
Sinn Fein president Mary Lou McDonald said: “Sympathies and prayers with family, friends and colleagues of the garda officer killed last night.
“A shocking, senseless loss.”