Fianna Fáil Senator Ned O'Sullivan has revealed he was physically threatened by an anonymous contributor to social media.
“Something needs to be done,” he said. “Eventually, something will have to be done to protect the rights of individuals.”
Mr O’Sullivan told the Seanad on Thursday he had personal experience of the negative aspects of social media when he had, “famously, or perhaps infamously”, made a comment about the seagull situation in Dublin.
He said his family had been subjected to a "horrendous'' campaign of abuse on Facebook for a week afterwards.
One person had suggested, “in quite a detailed manner”, he should be physically assaulted.
“It was terribly upsetting because at the time I did not quite understand that type of comment,” said Mr O’Sullivan.
“I did speak subsequently about it here in the Seanad and, of course, I drew all the trolls on me again.”
Mr O'Sullivan said those wishing to express an opinion, by way of writing to The Irish Times or some other publication, had to give their names and stand over the views expressed.
“I have no problem whatsoever with that,” he added.
“These nameless, faceless people, who obviously have no lives to live of their own and spend their entire time on their computers watching to see who they can attack or abuse next, are different.”
Fine Gael Senator Ray Butler said Facebook should be accountable for its content.
“I have no problem with community pages that include the correct type of news, but when we have these trolls, as I call them, putting false news about people on these pages, it is not right and there must be accountability,” he added.