The Dáil has heard claims that the family at the centre of a termination case at the National Maternity Hospital believes an "illegal abortion" was carried out.
The allegations were made by Aontú TD Peadar Tóibín under Dáil privilege.
Details of the case in question emerged recently.
The couple opted to have a termination after they were told their unborn baby would not survive, following two test results indicating the unborn baby had an abnormality.
Results from a third test - which came back after an abortion was performed - showed there was no abnormality present.
Speaking in the Dáil today, Deputy Tóibín claimed he was in contact with the family's legal representative.
He alleged: “The family are stating that this was an illegal abortion.
"They stated that the medical practitioner who signed off on the abortion never examined the mother in question nor even met with the mother in question in advance of the abortion. If this is the case, Taoiseach, than it is contrary to the law that you brought in and it is in fact illegal."
He further claimed: “The family have stated that they have been ignored by the government, with regards to their calls for an independent investigation. They said they have had no real input into the terms of reference of the internal review that you are planning.
"They are also shocked at the allegations that have been made that the medical practitioners that sign off on the abortions have also got a commercial interest in the companies that have produced the fatally insufficient tests in the first place."
Responding to Deputy Tóibín's remarks, Taoiseach Leo Varadkar said it was an individual case and a private matter.
He said: "I'm not party to all of the information either from the family affected or from the hospital's side either.
"I really don't 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 underway."
He added that he believes the Health Minister 'wants and expects' an external inquiry to be carried out.
In a statement, the National Maternity Hospital disputed some of Deputy Tóibín's comments.
A spokesperson said: “The National Maternity Hospital, despite what was alleged by Peadar Tóibín in the Dáil today, is actively engaged in commissioning an external review of this sensitive case."
Last week, the UK's Royal College of Obstetricians and Gynaecologists (RCOG) said it was unable to carry out a review despite a request from the NMH.
The NMH says the family has been informed of that, and since then "significant progress" has since been made with the RCOG regarding the membership of an external review and terms of reference.
According to today's statement, they hope to finalise details of the review shortly.
The spokesperson adds: "It was not the hospital’s intention to make any comment at this stage but we felt it necessary to respond to matters stated under parliamentary privilege which the Deputy suggests is an account given to him by a legal representative of the family."