The GHRC comprising its chairman A D Salkar and member J A Keny issued the order on a petition filed by social activist Aires Rodrigues.
The body is lying in the state-run Goa Medical College and Hospital morgue since November 7, 2015.
Rodrigues, in his complaint to the GHRC in March this year, had said the body of Dias, who was found dead at St Estevam, was kept in the "unhygienic and regularly malfunctional" morgue infested with rats and sought its disposal.
Rodrigues had contended that the performance of the priest's last rites should not be further delayed as all forensic tests had been done and the viscera report received by the Crime Branch which was investigating the case.
He said the last rites cannot be kept pending indefinitely. The petitioner said if nobody comes forward to claim the body, it would be a social responsibility to ensure that his human rights are not violated any further.