Simon Harris has hit out at the “despicable” threats against his children.
In a statement on social media, the Tánaiste and Fine Gael leader said the threats had been received over the weekend and were “unacceptable in every way”.
The posts have since been reported to An Garda Síochána.
“Let me be clear: threatening people - any person - is a crime,” he wrote.
“Threatening children is despicable. It is cowardice and it is a line that no decent society should tolerate being crossed.”
Minister Harris added that he would not comment further while the Garda investigation is underway.

On The Pat Kenny Show, Newstalk Political Correspondent Seán Defoe said it is likely the posts posed a “very serious, credible threat” to the Harris family.
“The level to which this is being taken and having counter terror Gardaí looking into this as well is a level above what we usually see,” he explained.
“We don’t know exactly what the post was or what the complaint had been.
“We do know from what Simon Harris has said this morning is that it is in relation to his children.
“He has had a number of posts on social media recently about his children; one where they were in his office with him, another a back to school post.
“Very normal things that he puts up; he features his family quite prominently.
“He’s gotten quite a bit of abuse under those for the case of Harvey Morrison and his tragic death.”
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Seán added that unless the person behind the posts is a real “tech wizz” it is likely Gardaí will be able to track them down.
“I think when you have this level of Gardaí, it’s very difficult to hide unless they are someone who is very sophisticated," he explained.
“They are good at finding these accounts, more so now as we’d seen various cases of defamation online from anonymous accounts.
“This is something they deal with relatively regularly.”
Taoiseach Micheál Martin has condemned the threats against Minister Harris’ family as “abhorrent”.
“Such threats to people in public life are unacceptable,” he said.
“They are a fundamental threat to our democracy.”
Main image: Simon Harris. Picture by: RollingNews.ie.