The State's agencies showed a "shameful'' lack of empathy with Joanne Hayes, Fianna Fáil leader Micheál Martin told the Dáil.
He said it was a damning indictment of those institutions and society at the time.
Ms Hayes received an apology from An Garda Síochána on Tuesday about the botched investigation into the discovery of a baby's remains on White Strand beach near Cahersiveen in April 1984.
She was wrongly charged with the murder of ‘Baby John’, who was found with 28 stab wounds, with Garda investigators suspecting the then 24-year-old from Abbeydorney, about 75km from White Strand, had given birth to the baby and killed him.
“She was wrongly accused of murdering a baby and was put through a horrendous tribunal which was meant to inquire into the failures of An Garda Síochána in its conduct of the investigation but which essentially turned into a cross-examination of Joanne Hayes herself.’’
He said the State should “adequately and properly’’ compensate Ms Hayes for what happened.
“The State should not put her under duress or force here to go through any process but should do the honourable thing by acknowledging the terrible hurt that was caused and providing adequate, appropriate and fair compensation,’’ he added.
Tánaiste Simon Coveney said the Government would try to make a quick decision on the matter of compensation.
“We will certainly try and deal with this issue in as sensitive a manner as possible,’’ he added.
He said he was not at liberty right now to say how this would take place.
Mr Coveney welcomed the Garda apology to Ms Hayes.
“I also want to join the Minister for Justice and the Taoiseach in apologising on behalf of the State,’’ he added.
A very different Ireland
Mr Coveney said he was starting secondary school when the Kerry babies tribunal was held.
He would like to think, he added, it was a very different Ireland in approach to women and pregnancy in those days.
“However, I also accept the point that real policing mistakes were made,’’ he added.
“There were also mistakes made in the subsequent tribunal in terms of how a woman and her family were questioned.’’
In the Seanad, Fianna Fáil's Catherine Ardagh said she was two years old when the tribunal was held and she had learned from journalists who had covered it how Ms Hayes had been bullied by gardaí and coerced into signing statements.
“The mind boggles; it was like seeing a horror movie mixed with an episode of ’Father Ted’,’’ Ms Ardagh added.
Sinn Féin’s Rose Conway-Walsh said she wanted to acknowledge the “absolute injustice and torture” Ms Hayes had suffered at the hands of State institutions.
“One can only come to the conclusion that there was absolute collusion between individuals working in those institutions to be complicit in her torture over months and years,’’ she added.
She said there should be an inquiry into the behaviour of those involved in making the decisions leading to the ill-treatment of Ms Hayes.
Independent Frances Black said the methods used by the gardaí to extract confessions should also be investigated.
Labour's Ivana Bacik said she also wanted to express solidarity with Ms Hayes and her family.
“Like others, I was too young to know the details of the case at the time,’’ Ms Bacik added.
“I do remember in school hearing about it and being aware even then of the immensely brutal way in which Ms Hayes was treated by the gardaí.’’