According to the the spokesman of the Public Authority for Search and Identification of Missing Persons, Abdulaziz Al-Jaafari, a body has been recovered from the site not far from the city.
In a statement Jaafari said search teams had dug up the remains from the grave,
He said a search operations is currently underway to find other suspected bodies buried at the site.
The new discovery comes more than two months after a mass grave was found in the city in the wake of a retreat by Hafter's troops after a successful onslaught from forces backing the internationally recognised Government of National Accord.
Until their retreat, Tarhouna was the main stronghold of Hafter's forces in western Libya.