The Ministry of Defense (MoD) said the gun battle between the militants and Afghan forces erupted during a clearance operation in Chak district.
A statement by MoD said the operations were conducted as part of Badr Operation of 203rd Corps of Afghan National Army.
At least 4 motorcycles used by the anti-government armed militants were also destroyed during the operation, MoD added.
The anti-government armed militant groups including the Taliban insurgents have not commented regarding the report so far.
Meanwhile, MoD said a Taliban insurgent who was wounded during an airstrike b coalition forces in Hesarak district of Nangarhar province was arrested by the Afghan army.
MoD also added that a child was injured after a mortar round fired by militants landed on a residential house in Geyan district of Paktika.
The Afghan armed forces also discovered 8 Improvised Explosive Device (IED) during separate operations conducted in Khost, Paktika, Logar and Maidan Wardak provinces, MOD said.