Health Minister Simon Harris has said an external review "is warranted" into an abortion carried out at the National Maternity Hospital.
It is reported the woman involved in the case underwent tests which can identify an abnormality that can lead to Edwards' Syndrome.
That is where the baby is often born small and with heart defects.
Three tests were carried out.
While the first two indicated Edward’s Syndrome, the third found the unborn baby did not have the genetic disorder.
The final test results came back after the termination.
It is standard practice here for a decision on terminations to be made based on the first result.
The couple have now made a complaint.
In a statement, the Holles Street Hospital said earlier: "We cannot comment on individual cases.
"We can confirm that we have asked the Royal College of Obstetricians and Gynaecologist to conduct an independent review of a recent case at the hospital."
A statement on behalf of Minister Harris said: "The minister's overriding concern is for the couple involved and respecting their privacy .
"The minister believes that an appropriate external review is warranted into the matters that arise here and it is important to await its findings."
Full investigation
This evening, a solicitor for the couple at the centre of the case said they are "utterly devastated" and are calling for a full review of the case.
Caoimhe Haughey said the couple are still grieving.
“This couple are absolutely devastated and have suffered just catastrophic shock,” she said.
“On top of grieving and being in the process of a bereavement for their much-wanted baby, to learn that their baby [...] did not have this genetic disorder that they were led to believe.”
She said they need details on how any review would be conducted.
"Clearly this couple want to get honest answers and they want to get to the truth of how this happened and why it happened,” she said.
“But what is really extraordinary about this couple is that they want to make sure that this never happens again to another mother or another couple in this country.
“They are very strong about that.”
Discussions with RCOG
The UK's Royal College of Obstetricians and Gynaecologists (RCOG) said it had not yet been formally asked to conduct a review into the case.
It added that any approach "will be considered in the usual way".
In a later statement, Holles Street clarified that "our discussions with RCOG in relation to a review of this matter are continuing."
"Very distressing"
This afternoon, the Taoiseach Leo Varadkar said his heart goes out to the couple involved.
“What I have heard is very distressing,” he said.
“My heart goes out to the couple who are at the centre of this.
“As these matters are private and personal and confidential - I don’t have any access to the details - and I think it is important that we respect the fact that these matters are private and personal and confidential – at least until such time as the couple decide otherwise.”
"Incredibly rare"
Speaking on the Pat Kenny Show earlier, Master of the Rotunda Professor Fergal Malone said issues with testing are "incredibly rare".
The consultant obstetrician explained: "It is important to realise it is very rare to have discrepant results.
"Different labs have slightly different ways of testing - some labs quote about a one in a thousand risk of [a] discrepancy happening, other labs quote as low as one in 10,000."
Additional reporting: Jack Quann
