The national news agency, Bangladesh Sangbad Sangstha, reported victims of the fighting, which began Sunday, included at least three police officers, a paramilitary trooper and a 12-year-old boy.
Police declared no rallies could occur Monday in Dhaka, CNN reported.
The ultra-conservative Hefazat-e-Islami gathered Sunday to demand the government enact laws that, among other things, would put to death anyone who blasphemed Islam, require mandatory Islamic education for all, ban statues and reinsert the phrase "absolute trust and faith in the almighty Allah" in the constitution, the report said.
Fighting broke out between protesters and police and paramilitary troops when Hefazat activists tried to breach a police barrier, witnesses said. Police fired rubber bullets and tear gas and activists threw rudimentary explosives and pieces of brick for hours.
The clashes in the Motijheel, Dhaka's commercial center, ended when about 10,000 security forces moved into the area Monday to disperse the crowd.
"The Motijheel is now under our control. ... Hefazat-e-Islami has quit the area," a police spokesman told reporters after the confrontation.
Syed Ashraful Islam, secretary-general of the ruling Awami League and a government minister, said demonstrators set fire to the Communist Party of Bangladesh office and ransacked businesses.
Shahriar Shahid, BSS managing editor, said the news agency temporarily suspended operations after Hefazat activists set a fire at its office's entrance.
Human rights groups said the Bangladeshi government shares blame for the crackdown and for stifling free speech of the Islamic group and others.
On Monday, authorities closed the offices of pro-Islamist Diganta Television after it aired video of the clashes, CNN said.
"They came in early in the morning and ordered us closed," staffer Tanvir Hussain told CNN.
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