The Tánaiste has described threats made against his family as "despicable" and said that threatening children "is a line no decent society should tolerate being crossed".
A threat made against Simon Harris and his family was posted on social media yesterday morning.
The Tánaiste alerted gardaí, who have confirmed a criminal investigation is under way.
In a statement this morning, Mr Harris said: "This weekend, I received direct threats targeting my family.
"As a father, I have very strong views and feelings on this as you can imagine. As a political leader, I find it unacceptable in every way.
"Let me be clear: threatening people - any person - is a crime. Threatening children is despicable. It is cowardice and it is a line that no decent society should tolerate being crossed."
The Tánaiste said he would not be commenting further as the garda investigation is ongoing.
The investigation is being conducted by gardaí from Wicklow and specialist units, including the National Cyber Crime Bureau and the Special Detective Unit.
It is not the first time Mr Harris has been threatened on social media, but gardaí say they are concerned about the nature of this threat.
Protesters have also previously turned up outside the family's home in Co Wicklow.
