Twenty of the injured were protesters and 15 were policemen. Later, police reportedly arrested seven protesters from the spot.
The incident took place when the protesters brought out a torchlight procession in the area around 7pm.
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Police obstructed them and detained some of the protesters from the spot, leading to a clash between two sides.
At one stage, Police fired teargas there, forcing the protesters to take position in front of the central mosque of Dhaka University.
Najifa Jannat, a spokesperson of the protesters, alleged that they brought out the torchlight procession from the Central Shaheed Minar and were marching towards Shahbagh via TSC.
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When they reached TSC area, police suddenly obstructed them and baton-charged to disperse them, leading to a scuffle.
According to Shahbagh Police Station sources, some four protesters were arrested from the spot, though the protesters claimed the number of arrestees to be seven.
Sajjadur Rahman, deputy commissioner of Dhaka Metropolitan Police (Ramna Zone), said that police showed utmost patience in tackling the situation.
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"The protesters were marching towards Shahbagh and we tried to disperse them. But they carried out attack and threw brickbats at us. Around 14 policemen, including me, sustained injuries in the incident," he said.
Samajtantrik Chhatra Front President Salman Siddiqui said some 20 protesters were injured in the clash. He also announced that the protesting organisations will bring out a rally from the Raju Memorial Sculpture tomorrow noon, protesting against the police attack on them.
Writer Mushtaq, who was detained in a case under Digital Security Act (DSA) last year, fell sick in Kashimpur jail and later died on Thursday.
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The death triggered much outcry in the country, especially on the social media platforms, as he had been languishing in jail in a case filed under the Digital Security Act.