President Mikheil Saakashvili ordered police deployed to all jails to replace prison guards amid tension set off when opposition television channels broadcast a video last week showing guards torturing inmates at a Tbilisi jail.
The scandal erupted just days before the October 1 parliamentary elections.
Tugushi's predecessor and the interior minister both resigned in the wake of the scandal.
Tugushi said on September 25 that the situation in the country's prisons is now fully under control as "all prison officials involved in torturing inmates have been dismissed and are being prosecuted."
Tugushi said a special investigative committee will soon be set up to probe reported cases of prison torture.
Saakashvili's ruling United National Movement faces a challenge from the Georgian Dream opposition coalition of billionaire Bidzina Ivanishvili.