According to local government officials, the militants were killed in Manogi district following a drone strike on Tuesday morning.
Provincial security chief, Abdul Habib Syed Kheli confirming the report said the airstrike was carried out around 7 am local time in Manogi district.
Mr. Syed Kheli confirmed that the five militants including a senior Taliban were killed in the airstrike.
According to Syed Kheli, the Taliban leader who was killed in the airstrike was recognized as Haji Ataullah who was actively involved in anti-government armed attacks in this province.
Taliban militants have not commented regarding the report so far.
Kunar is among the volatile provinces in eastern Afghanistan where Taliban militants and insurgents from the other militant networks are openly operating.
Kunar is also considered to be a hotbed of insurgents both for the Afghan and Pakistani militants, as Kunar province has border with the tribal regions of Pakistan.