The 201st Silab Corps of the Afghan Military in the East said the incident took place on Saturday in the vicinity of Shegal district.
The source further added that the Afghan force responded to the militants attack in Shinkorak area using heavy and light weapons.
According to the Silab Corps, at least two militants were killed during the clashes and two others sustained injuries.
The security situation in eastern Kunar province has started to deteriorate sharply during the recent months amid growing insurgency activities by the Taliban and ISIS militants.
The US forces based in Afghanistan have carried out a series of airstrikes targeting the hideouts of the Islamic State of Iraq and Syria (ISIS) group in eastern Kunar province of Afghanistan last week, leaving at least five militants dead.
The 201st Silab Corps of the Afghan Military in the East said the latest airstrikes were carried out in Manogi and Narang district.