According to the local officials, scores of Taliban insurgents launched the attack in the early hours of Saturday to take control of security posts in Ghaziabad district.
The provincial governor Wahidullah Kalimzai however said the attack was launched late on Friday night and continued for several hours.
He said a member of the Afghan National Army lost his life and three others were wounded in the attack.
The Taliban group spokesman Zabiullah Mujahid has claimed that two Taliban militants were killed and five others were wounded during the gun battle with the Afghan forces.
Mujahid also claimed that eleven soldiers of the Afghan National Army were killed and several others were wounded during the clash.
Kunar is among the volatile provinces in eastern Afghanistan where anti-government armed militants are actively operating in its various districts.
The province is also home of various foreign insurgents as they are routinely crossing the Durand Line from the tribal regions of Pakistan to stage attacks.
The coordinated attack on security posts in Kunar comes as the Taliban group announced its summer offensive earlier last month and vowed to carry out more attacks across the country.