The bodies of 56-year-old Eileen O'Sullivan, her partner Mossie, and their 24-year-old son Jamie were found at the family home on Tuesday night.
The tragedy comes less than a year after the Kanturk murder suicide case.
Michael Martin says Government will need to reflect on the issue:
"I do think we need to evaluate and reflect on this. But I'd like to hear the full sort of analysis from all authorities from different disciplines and the Gardaí to try and get a sense of what happened here, it has happened elsewhere as well in the country in recent times, and it is a very significant worry. So I do think we need to reflect on that and learn lessons from it and then apply it in a number of areas."
