According to local security officials, the incident took place early on Saturday in Nari district.
Provincial police chief Gen. Abdul Habib Syed Khel said a group of Pakistani Taliban and Lashakr-e-Taiba militants launched coordinated attack on a number of security check posts early on Saturday.
Syed Khel further added two members of Afghan national security forces were also killed during the clashes.
The Taliban militants group claimed responsibility behind the incident and said at least three security check posts were occupied by Taliban fighters.
However, the local security officials rejected the Taliban claims for occupying the security check posts.
Kunar is among the volatile provinces in eastern Afghanistan where anti-government armed militant groups are actively operating in its various districts and frequently carry out insurgency activities.