Gardai say they are concerned for the welfare of a mother after a 13-week-old foetus was discovered.
A member of the public alerted officers to the remains outside a house near Dunkineely, Co Donegal, on Tuesday evening.
Medical tests were carried out in Letterkenny General Hospital where doctors were able to establish how far into pregnancy the woman may have been.
The discovery was made at a house in the townland of Brenter at about 5.15pm.
A Garda spokesman appealed for anyone with information to contact officers in Ballyshannon station where the matter will be dealt with sensitively.
"We are concerned for the welfare of the mother as she may need vital medical attention. We would ask that anybody with information comes forward and they will be treated in the strictest of confidence," he said.