Members of al-Qaida-linked Salafist Group for Preaching and Combat (GSPC) ambushed an army unit on patrol and killed two soldiers on Monday in Boumerdes, about 50km east of the capital Algiers, the Liberte newspaper said on Tuesday.
Five soldiers were also seriously wounded in the attack, the newspaper said citing unnamed sources.
Authorities were not immediately available for comment.
In a separate incident, two rebels suspected belonging to the smaller Armed Islamic Group (GIA) were killed late on Sunday during clashes with security forces near Chlef, about 200km southwest of Algiers, Liberte said.
GSPC and GIA fighters have stepped up attacks to try to sabotage an amnesty plan expected to be offered to rebels later this year.
The amnesty is meant to end more than a decade of violence, which has left up to 200,000 people dead and cost $30 billion in damage.
Rebels took up arms in 1992 after authorities cancelled legislative elections that a now-banned Islamist party was poised to win.
But violence has fallen sharply in recent years.