An 18-year-old man died after he was shot in M'Sila region southeast of the capital, Algiers, while a 32-year-old man was hit in the face by a tear gas canister.
20 other people are reported to have been injured in the clashes.
The deaths are being reported by the Arabic-language daily El Khabar and have yet to be confirmed by the authorities.
The violence is said to be linked to unemployment and the rising costs of staples including sugar, floor and oil.
Youths clashed with police in Algiers and several other towns across the country on Friday despite appeals for calm from Imams after several days of unrest.
The riots in the capital broke out after Friday prayers in a poor neighbourhood and continued throughout the night with protestors ransacking a local government office.
They also cut down electricity poles cutting off power to the working class suburb of Auzas.
According to the International Monetary Fund, about 75 per cent of Algerians are under the age of 30 and 20 per cent of youths are without jobs.