It follows confirmation on Friday that a "significant" number of infants and children were buried at a former mother and baby home in Tuam.
Frances Fitzgerald also told today's Sunday Independent that inquiries at other former homes around the country are also likely.
"No dodging. Ultimate either State responsibility to properly oversee these types of institutions and to hold those who were responsible for running the institutions to account.
"No suggesting that somehow this was about an impoverished society that couldn't care for children effectively."