Debesh Chandra Pramanik, 68, a shoe store owner, was murdered inside his shop in Gaibandha of northwestern Gobindaganj Upazila.
"We still do not have any reason to believe that Debesh Chandra Pramanik was killed by (Islamist) militants as it did not match the pattern which was seen in all the cases where they were involved," Gaibandha district police chief Ashraful Islam told PTI.
He made the remarks when asked about reports stating that the hand of Islamist militants was being suspected in Pramanik's murder.
"In all the cases of murder carried out by the suspected militants, the assailants appear on the crime scene on motorbikes, but no motorbike is used in this case," the police official said.
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Another senior officer in police's detective branch said, "Someone identifying them to be IS or al-Qaeda claim responsibility after every such murder by militants but no such claim has been made in Debesh's (murder) case."
The victim's family claimed that some local drug addicts tried to extort money from Pramanik a few days ago and when he refused to pay, an argument broke out at the shop.
Immediately after the murder, police arrested a man named Nepen Chandra in connection with the murder acting on allegations of the victim's family members.
Bangladesh recently has witnessed a wave of murders of liberal and secular activists, writers and minorities by suspected Islamist militants.
A Muslim homoeopath doctor being their last victim last week in western Kushtia.
The Islamic State reportedly claimed responsibilities of most of the murders but Bangladeshi authorities rejected the claims.
"The home grown militants are repeatedly trying to prove their links with international outfits like IS or al Qaeda," a senior home ministry official had said after last week's murder.
A Buddhist monk, a atheist student, two gay rights activists, a liberal professor, a Hindu tailor and a sufi Muslim leader were the other victims of the deadly attacks since last month.