Justice Minister Simon Harris has said it is a “pivotal moment” in the Kerry Babies case and has urged anyone with information to come forward.
It comes as gardaí are continuing to question a man and a woman who were arrested on suspicion of murder in the Kerry Babies case.
The body of a five-day-old baby was found on a beach in Caherciveen, Co Kerry, in April 1984. The body of the baby, later named John, was found with 28 stab wounds.
Mr Harris said it was important to remember “the most innocent of people, an innocent baby” was found murdered on a beach.
“And no matter how long ago it was, or how different in Ireland it may have been, every person young or old has a right to truth and justice,” Mr Harris said.
“And I know the gardaí has been working extraordinarily hard on this, particularly since a renewed effort in 2018.
“And anybody who has any information no matter how small, and that could be extremely helpful,” he said.
The Justice Minister, speaking on RTÉ's, he said he was “conscious of the fact” that this case was at a time that “really brought a lot of pain in terms of the biases that existed in Ireland.”
He said it was a “defining moment” in social history and said he was “very much” thinking of Joanne Hayes, who had been wrongly accused of the death of Baby John.
On January 16, 2018, gardaí announced a review into the death of Baby John following a Garda apology to the Kerry woman.
“I very much think of Joanne Hayes today and her own family and all of the pain that she went through and the really despicable and unacceptable way she was treated at this time," he added.
“And of course I think of her and couldn't imagine how painful a day like today must be for her.”
Echoing the Justice Minister's remarks, Taioseach Leo Varadkar called the arrests “a significant development".
Mr Varadkar said the case is “a really tragic case that everyone in the country is familiar with”.
Arriving at the second day of an EU summit in Brussels, Mr Varadkar said that while he had seen the news, “it is a live investigation so probably best [for me] not to say too much about it.”
Tánaiste Micheál Martin said that justice is required for Baby John and "closure for everybody" in a case which has caused "terrible trauma for so many families."
"It has been quite a shocking experience, particularly for Joanne Hayes and the people involved," he said.
"I'm not going to comment on the garda investigation but will await its outcome," he added.
"It is a case that has been there in the background for almost 40 years and huge sadness around it, terrible trauma for so many families.
"But certainly, justice is required and has been required for a long time, but also closure."