One policeman died and four more were wounded when a security forces patrol came under fire from rebels hiding on a road on Sunday night in Jijel province, around 350km east of the capital Algiers, El Khabar newspaper said on Tuesday.
Three civilians who were nearby were also wounded.
In a separate incident on the same day, fighters shot dead two people in the eastern province of Bmoumerdes, 50km from Algiers, El Watan daily reported.
Authorities were not immediately available for comment.
Algerians voted in a referendum in September to back a partial amnesty for rebels fighting for an Islamic state, in a drive to end more than a decade of civil war that has killed more than 150,000 people.
The Salafist Group for Preaching and Combat (GSPC), Algeria's largest outlawed movement, has rejected the offer, according to an Internet statement.