The Taoiseach Micheál Martin says gun ownership legislation needs to be evaluated, following the suspected double murder-suicide in Co Kerry.
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.
Gardaí are appealing to the public for any information as they search for a motive.
The tragedy comes less than a year after the Kanturk murder-suicide case, in which a father and his two sons died of gunshot wounds.
25-year-old Mark O'Sullivan was shot by his father 59-year-old Tadgh, and young brother 23-year-old Diarmuid, on October 26th of last year.
Mr Martin says the Government will need to reflect on the gun issue.
"My deepest sympathies go to the family of those who were killed and to the community.
"These are devastating events, and the enormity of them are quite shocking.
"I do think we need to evaluate and reflect on this - but I'd like to hear the full analysis from all authorities from different disciplines and the Gardaí, and try 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.
"I don't want to pre-empt what happened here, but I think we can't ignore events of this kind".
Additional reporting: Jack Quann
