Interior Minister Vano Merabishvili played the audiotapes at a news briefing in Tbilisi. He identified the mastermind of the recent unrest as Tariel Potskhveria, a Ukrainian-based Georgian criminal boss.
Merabishvili also said the tapes bring further evidence of an alleged opposition-sponsored plan to destabilize the country.
Georgian authorities say a riot broke out on March 27 at Tbilisi's Prison Number Five and that it aimed at aiding the escape of thousands of inmates.
Seven prisoners were killed when police quelled the unrest. Another 22 prisoners and 12 security officers were also wounded.
Parliament has rejected opposition demands that a probe be conducted into the incident.
(Imedi TV, Civil Georgia, Novosti-Gruziya)