The gun fight broke out last night after a road accident between the two sides in Lab-e-Jar area of the 15th police district in Kabul city.
Two persons were also injured in the gun fight.
The injured include another son of General Jurat and a supporter of Haji Rahim Puri.
Kabul police headquarters name the killed son of General Jurat as Nadim and the injured Tamim.
General Deen Muhammad Juran and Haji Rahim Puri are well known Jihadist commanders.
To prevent any unlikely violence, Kabul city had a tight security on Thursday following the incident.