Taoiseach Simon Harris has condemned what he called a trend of threatening and “dehumanising” politicians, saying it should not be accepted as normal.
Gardaí said they are investigating a threat made on social media against Mr Harris.
Several protests have been held outside the Taoiseach’s family home as well as the homes of ministers.
Politicians have voiced concerns against a recent coarsening of rhetoric against public representatives, and warned that the approachable nature of Irish politics was at risk.
In a statement released on Tuesday, Mr Harris said he did not wish to comment on his or his family’s security but wished to address emerging trends.
“The laws of the land apply to people online just as much as offline,” he said.
“There can be no hiding place for anyone seeking to threaten, attack or harm people or to incite others to do so.
“Politicians have become a regular target, and it is on the brink of being viewed as acceptable or a normal part of the job. It is not acceptable.
“I get up every day and go to work and work as hard as I can. So do most politicians I know from all parties, and none.
“Constant efforts to target us, demean us or dehumanise us should never be accepted, never be normalised, and always called out.
“I will never be deterred from doing my job as Taoiseach.
“Men and women of An Garda Síochána do us proud every day in their work and I thank them for that.
“I thank the people right across this country for their kindness and decency – it means the world to me and my family.”