The National Children's Hospital has said that after an "intensive medical investigation" the conjoined twins - born yesterday at Holles Street Hospital - were not suitable for separation surgery.
In a statement this evening, the Our Lady's Hospital for Sick Children in Crumlin said the twins remain in a critical condition.
They were delivered by caesarean section yesterday morning at the National Maternity Hospital, where their mother remains.
The parents have asked that the public "pray for the twins and all concerned at this difficult time".
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The hospital said: "The parents have also requested that their privacy be respected and the hospital will adhere to their wishes."
Conjoined twins occur in about one out of every 200,000 live births.