The 201st Silab Corps said the incident took place in the vicinity of Mamand Dara area of Achin district leaving nine militants dead from both sides.
The Silab Corps in a statement said at least three Lashkar-e-Islami and six ISIS militants were among those killed.
The statement further added that three Lashkar-e-Islam and four ISIS militants have also sustained injuries during the clash.
The ISIS loyalists have not commented regarding the clash with the Lashkar-e-Islam militants so far.
The latest clash takes place amid ongoing counter-terrorism operations against ISIS and militants affiliated with the other insurgent and terrorist groups.
Nangarhar has been among the relatively calm provinces since the fall of the Taliban regime but the militant and terrorist groups have been attempting to expand their foothold during the recent years.
However, the Afghan forces continue to their counter-terrorism operations to suppress the insurgency activities of the terrorist groups besides the US forces carry out regular airstrikes in support of the Afghan national defense and security forces.