The conjoined twins who were born in the National Maternity Hospital, Holles Street, Dublin, on Monday died late on Tuesday night.
They had been transferred to Our Lady's Hospital for Sick Children Crumlin in a critical condition after the birth.
Following intensive examination, a medical team decided the twins were not suitable to undergo an operation to separate them. It is understood they were joined at the abdomen and shared a liver.
Yesterday a spokeswoman for Our Lady's hospital said that the twins' parents had requested strict privacy at this time.
"We won't be issuing any bulletins, updates or statements at the parents' request," she said.
After the birth of the twins, the parents, who are from the midlands, had asked for people's prayers.
They knew in advance that the babies would be conjoined because of regular ultrasound scans taken during the pregnancy.
The babies were delivered by Caesarean section at 8.30am on Monday.
The birth of conjoined twins is a rare event, accounting for one in 50,000-100,000 births.
More than half are stillborn and one in three survive for only a few days after the birth. About 70 per cent of conjoined twins are female.
Both twins are always of the same sex.
