According to the officials, the clashes erupted in Khogyani district of the province inflicted casualties to the both terror groups.
The provincial government media office in a statement confirmed the new clashes and said at least five militants were killed and three others were wounded during the clashes.
The statement further added that the clashes erupted in Dar and Sikanadara areas of Wazir Tangi area.
Two militants were killed from the ISIS side while three Taliban insurgents including one of their local leaders identified as Ismail who was also famous as Fawad were among those killed, the provincial government added.
This comes as at least nine militants were killed in a similar incident in Nangarhar province on Sunday.
The latest clashes take place despite the call by the Taliban group leader Mullah Hebatullah Akhundzada to reach to an agreement for ceasefire, citing similarity of Jihadic efforts among the two groups.