Pro-choice groups are due to gather outside the Four Courts today to demonstrate their support for the 17-year-old at the centre of the abortion case.
Two groups, Choice Ireland and the Alliance for Choice, say decision to prevent Miss D travelling abroad for an abortion is a denial of basic human rights.
A spokeswoman said: "Miss D is another case of several that have gone before and will come again that highlight the flaws in Irish abortion law. Without legislation to deal with this issue, yet more Irish women in difficult situations will have to be dragged through the courts."
The Pro-Life Campaign, meanwhile, has welcomed the appointment of a senior counsel to represent the interests of the unborn in the High Court today.
Dr Ruth Cullen of the group said: "There are precedents for appointing advocates for the unborn in court cases. It is only proper that respect for the dignity and value of the unborn child be taken into consideration.
"The Pro-Life Campaign does not believe an abortion is in the best interests of either the mother or the unborn baby."
Yesterday's decision to appoint a senior counsel to represent the interests of the unborn child means the Attorney General will have two teams of lawyers at today's hearing: one representing the unborn and the other representing the Attorney General in his independent role as a constitutional officer.
Another pro-choice group, Doctors for Choice, called for Miss D to be allowed to have a safe and legal abortion in Ireland.
The group claimed that there was support from Irish obstetricians for this course of action.
"In 2002, two of the masters of the Dublin maternity hospitals acknowledged that they would prefer to see termination of pregnancy offered in Ireland, to women who are affected by fatal foetal anomaly," the group said in a statement.
"It is time to end the political hypocrisy surrounding . . . abortion and women's health care in this country. We call on the leaders of all political parties to respond to our statement that Miss D be offered a termination of pregnancy in Ireland."
