As some supporters of Ashraful tried to enter the area on Sunday, a clash with the Zakir Hasan group started and both the parties attacked with spears and fired bullets at each other, they said.
Rubel died on the spot after being hit by a bullet on the head and Mamun succumbed to his injuries at Bancharampur upazila health complex later.
Others injured in the clash are currently being treated at Narsingdi sadar hospital.
Ataur Rahman, inspector of Raipura police station said, "Rubel Mia's death was confirmed in the clash and his body is currently kept at Narsingdi sadar hospital. Another man's death was reported but could not be confirmed yet."
Police have been deployed in the area and the situation is currently under control, he said.