According to the local security officials, the militants were killed or injured in Chaparhar and Haska Mina districts on Sunday.
The provincial police commandment in a statement said a Taliban insurgent was killed in an airstrike conducted in Behmaro area of Chaparhar district.
No further details were given regarding the airstrike and it is yet not clear if the airstrike was carried out by the Afghan Air Force or the US forces based in Afghanistan.
Both the Afghan and US forces conduct regular operations against the militant groups in this province.
In the meantime, the statement, said a loyalist of ISIS terrorist group was wounded during a clash with the security forces in Haska Mina district.
The statement said the Afghan security forces and the local residents of the two districts did not suffer any casualties during the clash and airstrike.
The anti-government armed militant groups including the Taliban insurgents and ISIS loyalists have not commented regarding the report so far.
Nangarhar is among the relatively calm provinces in eastern Afghanistan but the anti-government armed militant groups have started activities in some of its remote districts during the recent years.