Tánaiste Simon Harris has said online threats to him and his family are a "clear and sinister pattern" to "intimidate" him out of public office.
Gardaí are investigating a threat made online to Mr Harris's family, the second in a week.
In a statement this afternoon, he said protecting his family will remain his "number one priority".
"I will be guided by them on the next steps," he said.
The latest online threat, which gardaí are treating as serious, was made against a member of his family on social media yesterday.
The Garda's Special Detective Unit which investigates extreme political activism and threats to the State, is carrying out a criminal investigation and has taken a statement from Mr Harris and the member of his family.
RTÉ News has learned the threat contained a serious and vile threat of violence with direct contact made with the close family member on the Meta platform.
In a statement, Meta said it does "not allow threats of violence on our platforms".
"We remove content and accounts that break our rules, as we have done in this case, and are continuing to work closely with law enforcement," a spokesperson said.
It is understood the threats were made even though the person is not a public figure and does not have an open or public profile on social media and is therefore difficult to contact directly.
In a statement this afternoon Garda Headquarters confirmed that An Garda Síochána is currently investigating this matter.
Mr Harris said what he and his family "have faced in recent weeks is not political debate".
"It is abuse," he said.
"It is intimidation. It is behaviour that should never, ever be treated as normal. And no one is to blame except those choosing to abuse and make threats."
"The threats made against my family are having deeply distressing consequences," Mr Harris added.
"Last week, direct threats were made against my children.
"And now, this weekend, late last night, vile and horrific threats were directed at a very close family member."
Mr Harris said he will consult with his party, Government and broader political colleagues about these these threats and "what action we can and should take".
Earlier this week, a woman in her 30s was arrested and questioned about threats to the family issued on Instagram last weekend.
She was released without charge pending a file to the Director of Public Prosecutions.
