The provincial government media office in a statement said the raid was conducted in the vicinity of Wazir area in Khogyani district, Khaama press reported.
The statement further added that a local commander of the Taliban group identified as Abdullah nom de guerre Mazlumyar was among the killed.
A large number of weapons, ammunition, and explosives of the Taliban insurgents were also destroyed during the operation, the statement added.
According to the provincial government, at least suspects were also rounded during the operation and are in custody of the NDS Special Forces for further interrogation.
The anti-government armed militant groups including Taliban insurgents have not commented regarding the report so far.
This comes as counter-terrorism operations are underway in a number of the districts of Nangarhar province against the Taliban and other militant and terrorist networks.
The anti-government armed elements have been attempting to expand foothold in some remote districts of the province during the recent years.