Provincial governor Mosa Khan Akbarzada confirming the report said the incident took place following verbal clashes among the Pakistan and Taliban fighters.
Mr. Akbarzada further added at least four people including two Pakistani Taliban and two Afghan Taliban militants were killed in Andar district in this province.
This comes as an Afghan Taliban leader was killed following clashes with the Pakistani Taliban militants in Quetta city of Pakistan recently.
In the meantime local authorities in western Farah province of Afghanistan announced at least 37 Taliban militants were killed or detained during special military operations by Afghan commandos.
A spokesman for the Afgan special forces Nastu Nasiri said the operations were conducted by Afghan and coalition security forces in Gulistan district on Sunday.
He said Afghan commandos and coalition security forces killed 7 Taliban militants and arrested 30 others during the operations without suffering any casualties and seized several weapons, ammunitions and explosives during the operations.
Gulistan distict is bordering southern Helmand province of Afghanistan and majority of the Taliban militants have reportedly fled to Helmand province as a result of the military operation.
Taliban militants group yet to comment regarding the reports.