The Taoiseach Enda Kenny says refugees must be allowed to seek asylum in Ireland to escape ISIS, who he says want to "blow up Newgrange".
Mr Kenny says the Co Meath monument, and the Rock of Cashel, would be offensive to Islamic State jihadists.
He has also tried to play down reports of a Coalition rift about the number of refugees Ireland can accept - with a special Cabinet meeting pencilled in for Thursday to discuss the issue.
He says the acts of ISIS in destroying ancient temples in Syria are a sign of their barbarism.
Mr Kenny said: "Look at what's happened in Syria with the growth of ISIS.
"Purely from the historical point of view, they want to blow up Newgrange and the Rock of Cashel, they want children shooting others in the head, this is horrendous."
The Taoiseach also said there is no split in Government over how many refugees Ireland will take.
Mr Kenny said he is not fixated on numbers, despite Tánaiste Joan Burton saying we should take 5,000.
A special meeting of the Cabinet is to be held this week to discuss Ireland's response.
Mr Kenny said: "When people say 'how many are you going to take in?' I want to see the European model here first of all.
"Why do they have to cross the sea at all, if you are in a position to assess if they are eligible for relocation or asylum status.
"don't be just fixated on a number, Ireland will do what it can."