Farhad Hossain Chowdhury, 55, and his adopted daughter Rupali Begum were found murdered last night in a Khanqah -- a building designed specifically for gatherings of a Sufi brotherhood -- close to the man's home in Dinajpur's Bochaganj upazila, about 350 kilometres north of Dhaka, police said.
"Both of them had bullet marks on their bodies and the young woman's neck was slit with a sharp weapon," Dhaka Tribune reported.
Farhad, a Pir or Sufi spiritual leader, was also the former president of Setabganj municipality unit of the opposition Bangladesh Nationalist Party (BNP) which is headed by former prime minister Khaleda Zia.
Bochaganj police station Officer-in-Charge Habibul Haque said the case was under investigation.
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Haque said that there had been no immediate clues to the means and motives of the murder. They suspect that it could be an Islamist extremist attack or result of a political or personal conflict.
"We are carrying out an inquest," the officer added.
Over a dozen Sufi Muslims have been found with their throats slit in Bangladesh since 2013. The authorities blamed homegrown Islamist extremists for the killings.