ATHENS, Greece -- Greek police said Tuesday the body of a 4-year-old Bulgarian girl believed to have been killed by her father will likely never be found due to the gruesome way in which her killer disposed of her remains.

A nation-wide hunt for young Anny, reported missing by her 25-year-old mother on April 24, ended Monday when both her parents were arrested and her father charged with murder and defiling a body.

Attica police chief Christos Papazafiri said the little girl was dismembered and her remains were dumped in various trash bins in Athens "in a way that it was not possible to determine they were body parts."

Papazafiri said the girl was believed to have been killed around April 8-9 and that her 27-year-old father confessed to disposing of his daughter's remains over several days. He said the child's body parts had been made to appear like thrown-away food leftovers.

Anny's mother, who repeatedly changed her testimony about how her daughter had gone missing, has also been arrested on charges of endangering a child. Authorities do not believe she knew about her partner's actions.

Police said they discovered Anny had been killed after blood traces matching the child were found in the pipes, on knives and in other parts of the family's central Athens apartment.

Authorities said that in recent weeks, the father had bought new furniture and cleaning material, sold his daughter's crib and stroller and was arranging to have the apartment pipes replaced.