Speaking late on Saturday, Uyahia said agreement had been reached on the so-called al-Kseur platform, which includes rights for the language spoken by the ethnic Berbers who inhabit the Kabylie region east of the capital Algiers.
The demands were first put forward in June 2001 by Kabylie's tribal leaders, known as aarchs, at a meeting in the village of al-Kseur.
The move followed widespread rioting sparked by the death in April 2001 of a teenager who had been arrested by gendarmes near Tizi Ouzou, the main town in the region.
An official statement issued after the talks, which had resumed on Friday after an interruption of almost a year, said: "The government and the aarchs have decided together to set up a joint mechanism to monitor implementation by the state of the al-Kseur platform."
The al-Kseur demands centred on recognition of the Berber culture and identity, and economic reforms for the Kabylie region.