The police, known as the Gardai, said "human limbs were found in a bag outside houses at the junction of Moatview Gardens and Drive" in the suburban area of Coolock near Dublin, The Irish Times reported.
The bag was found on a road by a group of young people, police said.
The bag reportedly contains arms and legs. Authorities are working with Forensic Science Ireland to identify all of its contents.
Investigators are also searching through missing person reports to determine the identity of the remains. Local officials suspect the remains are linked to rising drug crime in Dublin and surrounding towns.