Five others were also injured in the clash
The incident occurred on Thursday morning.
The deceased is Azim Mandal, 60.
The injured have been sent to Kushtia General Hospital.
Jahangir Arif, officer-in-charge (OC) of Kushtia Islami University police station, said Abdul Majid, a member of district unit Awami League and Abu Bakar Siddique, general secretary of Ujangram union Awami League, had been at loggerheads over establishing supremacy.
Azim Mandal, a supporter of Abdul Majid, was stabbed by supporters of Abu Bakar during the clash around 10am on Thursday. Five others were also injured in the clash.
On information, police went to the spot and brought the situation under control, the OC said.
Additional police have been deployed in the area to avert further trouble.
Abu Bakar has been detained, the OC added.