Minister for Justice Frances Fitzgerald has said she is concerned for the woman and baby at the centre of reports about the operation of the abortion legislation.
She said the Government will continue to monitor the law and see how it is implemented.
It was confirmed yesterday that a vulnerable young woman had a baby delivered by caesarean section after a panel of experts, convened under Ireland's new laws, decided not to permit an abortion.
Her case was assessed under the legislation, which was passed last summer and came into effect at the start of the year.
The woman cannot be identified as there is a court order in place with reporting restrictions.
A spokesperson for Minister for Health Leo Varadkar said he was made aware by the Health Service Executive that there was a situation and that it was being addressed.
He said the legislation is very clear that these are matters for clinicians.
Mr Varadkar said: "I do not wish to comment on any individual case.
"There are two very vulnerable people involved, a young woman and a little child. Neither should be seen as a news story or political cause.
"Both need care and compassion and I appeal to everyone to respect their privacy and anonymity."
Joint Oireachtas Committee Vice Chairperson on Health, Children and Youth Affairs Ciara Conway has said women's rights are once again being "trounced upon".
Deputy Conway said she is hugely concerned that such sensitive information has been leaked to the press.
She said her thoughts are with the young woman who had a very difficult choice to make and that choice was taken away from her.
The Labour deputy said: "I believe what we have seen the UN criticise Ireland for, that women are merely vessels and nothing more, I think we see that women's rights are once again being trounced upon".
She said she feels women will feel they have to travel abroad for abortions because of the level of scrutiny they face in Ireland and the media attention.
The National Women's Council of Ireland has said that a referendum is needed to repeal the eighth amendment now.
NWCI's head of outreach Rachel Doyle said: "No civilised society can stand over a law which sees a woman lose her bodily autonomy once pregnant.
"No more desperate women and girls should have to resort to the courts here and in the EU. The time for action is now."
The Pro Life Campaign has said this highlights the "horror and deep seated flaws" in the Government’s legislation.
Commenting on the case, Pro Life Campaign spokesperson, Dr Ruth Cullen said: "It is agreed on all sides that abortion is not a treatment for suicidal feelings."
She said: "The Government pressed ahead and railroaded through legislation that is not evidence-based and provides for abortion based on a threat of suicide."
Dr Cullen said: "We now have the situation where doctors are placed in the situation of making decisions knowing there is not a shred of evidence to back any of them up".
She said: "To put a defenceless baby through all this, and to pretend the intervention is medically indicated when it is known that there is no evidence to back it up, is a chilling aberration of law and medicine.
"The fact that the panel could just as easily have sanctioned an abortion in this case also brings home everything that is wrong about the new law.
"The Government successfully packaged the law as a life-saving measure even though it is nothing of the sort. Although it is going to take time, as more and more people begin to realise what the law actually provides for, support for it to be repealed will grow and grow."