A couple at the centre of a pregnancy termination case at the National Maternity Hospital wants an independent inquiry, after UK medical experts turned down a request to review what happened.
The couple says they were told their unborn baby would not survive.
It followed two test results indicating the unborn baby had Edwards Syndrome - a genetic disorder where the baby is often born small and with heart defects.
While the first two tests indicated the condition, results from a third showed there was no abnormality present.
The third test results came back after an abortion was performed.
Following a complaint, Holles Street hospital asked the Royal College of Obstetricians and Gynaecologists (RCOG) in London to review the case.
The expert group considered the request, but says in this particular case it is unable to carry out the review.
Instead, it has made alternative recommendations to the National Maternity Hospital.
A spokesperson for the RCOG said: "The RCOG has considered a request for an independent review of an abortion case at the National Maternity Hospital in Dublin. In this particular case, the RCOG is unable to undertake the review.
"The RCOG has made alternative recommendations to the National Maternity Hospital in order for the case to be reviewed independently and swiftly for the family and staff involved."
'Swift and immediate investigation'
Solicitor Caoimhe Haughey, who represents the couple at the centre of the case, says they now want the Health Minister to intervene.
She said: "They are extremely concerned, extremely worried that what has happened to them could happen to another couple, could happen to another mother.
"They have a heartfelt and genuine need for the minister to step up and have this investigated swiftly and immediately."
Explaining how an independent investigation would work, Ms Haughey explained: "You appoint a chairman... an expert... and a team of clinicians. Obviously in this instance it should be obstetricians, foetal medicine specialists and above all genetic expertise."
Health Minister Simon Harris has previously said he believes an "appropriate external review is warranted" in the case.