Afghanistan is experiencing its bloodiest period since US-led troops ousted the Taliban government in 2001.
Also in Kunar, a man shot and killed the police chief of Chawkey district on Friday night, General Abdul Jalal, the provincial police chief, said.
Governor Wahidi also alleged that US troops patrolling in the mountains on Friday had shot and killed a civilian and injured two others.
The US military, which has soldiers in the area, was unable to confirm the report.
In the western province of Farah, a suicide bomber with explosives strapped to his body blew himself up near a police vehicle.
Abdul Mutalib Rad, a regional police spokesman, said the bomber was the only person killed.
Rad also said that police arrested four men believed to be Taliban who were seen dropping the bomber off from a vehicle.
In another incident, a civilian truck driver was killed and a truck supplying Western troops was set ablaze in the southern province of Zabul on Saturday, police said.
A Taliban spokesman claimed responsibility.
Several Western politicians have recently warned that Afghanistan could slide back into anarchy if the worsening of the security situation is not controlled.