Taoiseach Leo Varadkar has said Majella Moynihan had her privacy invaded, she was made to feel shame, pressurised to give up her child and the way she was penalised was deeply sexist.
He said that what was done to Ms Moynihan was "wrong on every level."
He said that he has no difficulty in apologising on behalf of the State to her and other women treated similarly when all the facts of their cases are known.
He was responding to Sinn Féin leader Mary Lou McDonald who said people were "moved" and deeply saddened" by her story.
She said her story brought us back to that "awful mysoginistic" Ireland of the 1980s.
Ms McDonald said Ms Moynihan was "vilified, isolated and damaged in the most fundamental ways" because she was pregnant outside marriage as a member of An Garda Síochána.
She said that she was lucky she was not sacked because of the intervention of an Archbishop at the time.
She acknowledged that the Commissioner of An Garda Síochána Drew Harris and the Minister for Justice Charlie Flanagan have apologised to her.
She asked the Taoiseach to apologise to Ms Moynihan on behalf of the State.
She also pointed out that it has emerged that Michael Noonan, then Minister for Justice, in the early 1980s was contacted by Ms Moynihan but he said "this is an internal Garda matter."
She said the mind boggles as to how this case could have ever been viewed as an internal Garda matter.
The Sinn Féin leader asked if Michael Noonan would make a statement about those comments now.
The Taoiseach said he has not spoken to Mr Noonan about the matter and "I don't know if there are more Majellas out there. There may well be. Certainly I would have no difficultly apologising to those women on behalf of the State. But I would like to know the facts".
He said "this is very much a story that has gripped the nation in the last few days. I want to pay tribute to the RTÉ Documentary on One team for once again putting together a really fascinating programme that gives us further insight into our country and into our past. It is a true example of public service broadcasting."
He said that the documentary was "deeply moving" and "almost unbelievable" and what was done to Ms Moynihan was "wrong on every level."
"Her privacy was invaded; she was made to feel shame; she was pressurised to give up her child and the way she was penalised was deeply sexist, when you consider that the man involved was only subject to a fine."
He said that Minister Flanagan and Garda Commissioner Drew Harris will meet Ms Moynihan.
He said that this is the next step that should take place.
Ms McDonald said that she should be paid her full pension.
She added that it seems anecdotally that this was not an isolated case and if there are more women who were treated the same way.
She repeated that Michael Noonan should be asked to make a statement and explain his reported comments that the case was "an internal Garda matter."
Mr Varadkar said that this is not about trying to have a go at a politician. He said that this is about Majella Moynihan and her story and offering her an apology.
Meanwhile. Justice Minister Charlie Flanagan has said he expects the issue of Majella Moynihan's pension to be discussed when she meets the Garda Commissioner, Drew Harris.
During a Topical Issues debate in the Dáil, Mr Flanagan said he intends to apologise in person to Ms Moynihan when he meets her in the coming days.
"Various issues have been raised in relation to this case including the question of Ms Moynihan's pension. I expect this issue to be examined and discussed when Ms Moynihan meets the Commissioner. I do not intend to pre-empt that discussion. I would just caution that the situation is a complex one," Mr Flanagan said.
The matter was raised by Fianna Fáil TD Jim Callaghan, Social Democrat TD Catherine Murphy and Fine Gael TD Kate O'Connell.
Mr Flanagan told Ms Murphy that it was possible that there other similar cases, however, he said he was not aware of any at this time.