JI activists have been staging countrywide strikes for months to protest against ongoing war crimes trial in cases dating back to the 1971 independence war.
The clashes broke out when police raided a village in northwestern Chapainawabganj district to arrest a party activist accused of torching a power plant during the last month shutdown.
Hundreds of Jamaat and BNP activists from the adjacent villages gathered at the site and tried to snatch the accused from police, forcing them to open fire and lob teargas shells, ASP Ashok Kumar Pal was quoted as saying by bdnews24.Com.
At least 10 people including journalists were also injured in the clashes. Upazila Awami League General Secretary Gazi Fazlur Rahman was also injured.
In another incident in northwestern Sirajganj district, two Jamaat supporters died after being hit with bullets, local official said.
The opposition Bangladesh Nationalist Party was waging a campaign over electoral system demanding restoration of a caretaker government for election oversight as the national election was due next year, but ongoing trials of several stalwarts of its crucial rightwing ally Jamaat-e-Islami for 1971 war crimes has visibly shifted the focus.