The Irish Government is not obliged to allow unrestricted access to abortion during early pregnancy, campaigners said.
LoveBoth attempted to "save" the Eighth Amendment constitutional restrictions ahead of last month's repeal referendum on grounds that protecting the unborn's right to life was sacrosanct.
New legislation implementing the poll's overwhelming two-to-one verdict in favour of making the procedure available will be implemented in the new year, the Taoiseach has said.
Caroline Simons, legal consultant to LoveBoth, said: "We do not believe however that there is any obligation on the Government to legislate for unrestricted abortion in the first 12 weeks of pregnancy.
"When examined closely, providing abortion on such grounds would fly in the face of the Taoiseach's commitment that any new law would be restrictive and that abortion would be rare."
Ireland voted resoundingly to reform its strict abortion laws in last month's referendum, paving the way for the removal of the Eighth - the constitution's all but blanket ban on terminations.
Health Minister Simon Harris is to draft legislation that would allow abortions within the first 12 weeks of pregnancy, subject to medical advice and a cooling-off period, and up to 24 weeks in exceptional circumstances.
Ms Simons urged the provision of counselling services ensuring women with unplanned pregnancies were aware of all alternatives to abortion.
She said pain relief should be administered to the baby prior to a termination if there was a risk of pain.
Doctors should strive to preserve the lives of babies born alive following the procedure, she said, and warned against prenatal "discrimination" against the unborn on the basis of sex or disability.
"Provision should be made for the exercise of conscientious objection by healthcare professionals and by others working in healthcare facilities."
She said foetal remains should be disposed of in a fashion respecting the dignity of the unborn.
Pregnant women should have access to emergency care in hospital in case of complications, the organisation said.
British Prime Minister Theresa May has been under pressure to intervene to liberalise Northern Ireland's strict abortion laws following the Irish result.
Northern Ireland is the only part of the UK where the procedure is banned except in exceptional circumstances.
Leo Varadkar has said the Dail may have to sit longer into the summer to facilitate the passage of new laws in the Republic.