The operations were launched in Pechigram district earlier on Thursday and continued until late night of the same day.
Provincial police spokesman Hazrat Hussain Mashriqwal said the operations covered various parts of Pechigram district where anti-government armed militants were opearting.
Mashriqwal further added at least 16 anti-government armed militants were also injured during the operations.
The anti-government armed militant groups have not commented regarding the report so far.
Nangarhar is among the relatively volatile provinces in eastern Afghanistan where anti-government armed militants are actively operating in a number of its remote districts and often carry out insurgency activities.