Two homemade bombs exploded at Shahbag Square just after a procession, staged by youngsters belonging to Ganajagaran Mancha, protesting the strike passed the scene.
"None was hurt as the bombs were blasted near the Shahbag Police Station," said a police officer, adding that two motorcyclist hurled the bombs and fled the scene immediately.
Protesters clashed with police in several towns and set several vehicles on fire to enforce the strike. Shops and schools were closed here and major roads were largely deserted.
Violence was also reported from some other parts of the country, including southeastern town of Laksam, where police fired rubber bullets to disperse right-wing activists.
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The latest Jamaat shutdown comes a day after a special tribunal which deals with war crime cases, sentenced two Jamaat leaders to three months in jail for their derogatory and contemptuous remarks about the trial of several stalwarts of the party which was opposed to Bangladesh's struggle for independence.
Jamaat lawmaker Hamidur Rahman Azad and the party's acting deputy Rafiqul Islam Khan were sentenced in absentia by the controversial International Crimes Tribunal, which is trying Islamists and others for war crimes.