Tánaiste Simon Harris said he is doing his "very best to get on with my job" after a series of threats were made against him and his family.
Gardaí are investigating the threatening calls made to Mr Harris and his family.
It is understood the calls, which included bomb threats, were made on Telegram, which offers security provisions and encryption, enabling callers to disguise their identity.
The threats were phoned in to garda stations in Wicklow and Wexford in what appeared to be an orchestrated campaign against the Tánaiste and his family.
It was the third such threat to the family in a week.
We need your consent to load this rte-player contentWe use rte-player to manage extra content that can set cookies on your device and collect data about your activity. Please review their details and accept them to load the content.Manage Preferences
A direct threat was made online to a close member of his family last Friday and earlier last week another online threat was made to his children.
Speaking on RTÉ's Morning Ireland, the Fine Gael leader said it has been "a pretty rotten time" for him and his family and the threats could not be ignored.
"The vile nature of the threats targeting my children, very close family relatives and the sustained, relentless nature of it, I think and thought needs to be called out.
"This is not who we are. These are criminal acts and whatever people think of anybody's politics, I'm a democratically elected member of Dáil Éireann, I'm the leader of a political party and the Tánaiste of this Government," Mr Harris said.
He added: "People are entitled to go about their business, as are their families, and free from abuse and criminal behaviour."
The Wicklow TD said that he loves public service and that he has not considered leaving his role.
"I don't mean to be alarmist, but we've seen in other jurisdictions, violence against politicians. We've seen in this country violence against politicians.
"And I have a number of jobs. My job as a public representative and my job as a father, and a husband, and I'm trying to balance all of them. But like I say, I've dug deep, I've turned up and I'm trying to get on with the job.
