Tánaiste Simon Harris has said he is not willing to maintain "a dignified silence" in relation to threats made against him and his family.
She has since been released from custody and a file will be prepared for the Director of Public Prosecutions.
Speaking outside Cabinet, the Tánaiste said the threat is "really difficult".
"And you are meant to maintain a dignified silence in relation to all of these things and I am just not willing to do it anymore. I am just not willing to do this anymore," he said.
Mr Harris said it is deeply upsetting when it happens, specifically "when you experience direct threats to your children, to their safety".
He said he worries about the level of toxicity and also that someone can create an anonymous account and decide to target children.
He said for far too long "we have maintained dignified silence on this" and it is time for everyone in public life to say "enough".
He said it deserves consideration by policymakers and should be challenged by everyone.
"This is not who we are as a country, and I know that," Mr Harris said.
He said it does not matter where the threats happen, whether online, offline, anonymously or in person.
"We just can't have some sort of tolerance where we differentiate," he said.
"In many ways we are trying to apply 20th century policies and laws to the 21st century and I think that needs to be considered."
He said a garda investigation is continuing into the threat against his family.
