Two Islamist demonstrators, including a minor, were killed in police firing when several thousand Islamists attacked police with sticks, machetes and crude bombs in southwestern Satkhita, officials and reports said.
"They (Jamaat) activists violently attacked us with lethal weapons and homemade bombs... We were forced to fire gunshots for our defence when the two died," a police officer said.
In a separate incident, a 9-year-old girl was run over by a speeding bus that was being chased by protesters in suburban Gazipur. Another person died after being allegedly attacked by rival activists at southwestern Dinajpur.
Jamaat rejected the International Crimes Tribunal verdict saying it was delivered as part of a plot to eliminate their leadership as it called for a nationwide strike today.
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Businesses and shops were shut country-wide for the strike which started yesterday and roads and highways were largely empty, bringing inter-district transport to a halt.
Security was tight in the capital Dhaka, with thousands of police patrolling the streets.
Jamaat's crucial ally main opposition Bangladesh Nationalist Party (BNP), however, declined to make any comment on the judgement.
Azam is the fifth Jamaat-e-Islami politician to be convicted by the International Crimes Tribunal since the trial of war crimes suspects, mostly belonging to the Islamist group, began three years ago.