The Health Service Executive will ask the High Court on Thursday for an order allowing it to give a blood transfusion to severely anaemic twin babies after they are born.
The court heard this afternoon that their mother, who is 32 weeks pregnant, has objected to them receiving what has been described as a vital blood transfusion.
The mother has been attending Cork University Hospital.
Ms Justice Mary Laffoy heard that she and her partner have made it clear they object to any transfusion on religious grounds.
It is believed the parents are members of the Jehovah Witness Congregation.
The HSE believes the babies are at risk and should be delivered before the weekend.
The court was told they are severely anaemic and the mother has not objected to them being induced later in the week.
Ms Justice Laffoy granted the HSE leave to give notice to the mother and father of the executive's intention to apply for the order on Thursday.
The court also granted a temporary order restraining publication of the parents' names.