Mullah Malik and Mullah Wakil, who were senior Taliban leaders in the neighboring Farah province, were reportedly killed during the clashes, which also left 65 people wounded. The clashes are continuing, according to the newspaper.
The publication stated, citing local officials, that fighting broke out between groups loyal to high-ranking Taliban leaders Mullah Samad and Mullah Nangialai.
Recent infighting between Taliban factions was first reported in late 2015, when Taliban loyalists clashed with a splinter group aligned with the Islamic State (Daesh).
The Taliban has also faced a leadership struggle since the death of former leader and Emir of Afghanistan Mohammed Omar in 2013.
Afghanistan is experiencing political, social and security instability, as the Taliban movement and other radical extremist organizations such as the Daesh, prohibited in many countries, including the United States, the United Kingdom and Russia, continue staging attacks against civilian and government targets.