Police fired rubber bullets and tear gas canisters to disperse Islamists backed by Jamaat-e-Islami (JI) party whose leaders are facing trial in special tribunals for "crimes against humanity" during the 1971 liberation war against Pakistan.
While two deaths were reported from western Jhinaidah and northeaster Sylhet, two others died in northwestern Gaibandha.
Parts of the capital Dhaka and southeastern port city of Chittagong turned into battlefields as protesters attacked police, damaged or torched shops and vehicles.
Several worshippers were trapped inside the mosque as police tried to thwart the protest by locking the gates.
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Doctors at Dhaka's main state-run Medical College Hospital said they were treating several people with critical wounds caused by rubber bullets.
Newly formed "12 Like Minded Islamic Parties", backed by JI, took to the street after Friday prayers in the capital and other cities and attacked journalists.
At least 20 reporters covering the violence were injured, journalist union said.