The provincial police chief in a statement confirmed the incident, saying the incident occurred in the vicinity of Khogyani district of Nangarhar.
The statement said five Taliban militants including a local leader killed in the attack.
The key Taliban leader identified as Fazal Subhan had the responsibility of battle leadership in five border districts of the province.
The Taliban could not be reached for comments about the incident.
The security situation in Nangarhar province deteriorated during the recent years with the rampant insurgency led both the Taliban and ISIS militants.