Reports suggest that the scope of war between these militant groups have extended to Alingar district of neighboring Laghman province.
Sources in southern Nangarhar province say that the two extremist groups are inviting fresh fighters against each other from surrounding areas.
But officials in the Afghan Defense Ministry (MoD) say that Taliban and Daesh is only fighting in Khogyani district of Nangarhar province.
MoD deputy spokesman, Mohammad Radmanish told Ariana News that Afghan forces are trying to defeat the insurgent groups in the district and ensure the security for its inhabitants.
This comes as the Daesh militant group have launched efforts to expand its activities in the east of Afghanistan.
At least 11 Chechen nationals were arrested with weapons by Afghan security forces in Logar province on Wednesday as they were coming from Hesarak and Khogyani districts where the so-called Islamic State also known as Daesh have a strong presence.