A termination of pregnancy at the National Maternity Hospital for a fatal foetal abnormality has been raised in the Dáil.
TD Peadar Tóibín of the Aontú party said the family involved felt ignored by the Government in their calls for an independent investigation.
Speaking under Dáil privilege, Mr Tóibín made serious allegations about the case and raised claims that the medical professionals that are signing off on the abortions had also got a commercial interest in the companies that had produced the tests in the first place.
Responding to Mr Tóibín, Taoiseach Leo Varadkar said that was an individual case and a private matter, and he was not party to all of the information from the family affected or from the hospital's side.
He said he did not want to get involved in commenting on an individual case, even one that is very, very sad such as this, particularly when there may be legal proceedings under way.
The Taoiseach said he understood that Minister for Health Simon Harris wants and expects that an external inquiry will be carried out into the facts of the case.
Mr Tóibín also questioned whether procedures for signing off on termination of pregnancy in the case were fully followed.
Last month, RTÉ News revealed the case of a termination of pregnancy at Holles Street in what was believed to be a case of a fatal foetal abnormality.
The couple said they were advised that the baby had Trisomy18, also known as Edwards Syndrome, and that it would not survive.
The decision to proceed to a termination followed a series of tests.
When the results of a final test came through, after the termination in March, it showed the baby did not have the fatal foetal abnormality.
Holles Street Hospital has been working on securing a team of experts to conduct an independent review of the case to establish the facts.
In a statement, the National Maternity Hospital said that despite what was alleged by Mr Tóibín in the Dáil, the hospital is "actively engaged in commissioning an external review of this sensitive case".
It said the family was informed that the Royal College of Obstetricians and Gynaecologists in the UK had been requested to perform the external review, but it was not in a position to do so.
Since then, significant progress had been made with RCOG in respect of membership of the external review and the terms of reference.
The hospital said it hoped to be in a position to finalise these shortly.
Holles Street said it was not its intention to make any comment at this stage, but felt it necessary to respond to matters stated under parliamentary privilege, which Mr Tóibín suggested was an account given to him by a legal representative of the family.
The hospital said it is not its intention to comment further, pending the outcome of the review.
Additional reporting Conor McMorrow