No injuries were immediately reported in the clashes Tuesday in the Dhanmandi and Mirpur districts in central Dhaka.
The violence occurred after about 1,000 demonstrators tried to march into the streets for the strike called by a 14-party opposition alliance to protest the death of activist Golam Rasul Milon.
The opposition alleges Milon was fatally hit by a tear gas canister police fired during a violent, anti-government protest in the Bangladeshi capital Sunday. Police, however, say Milon died of a heart attack.
On Tuesday, authorities stepped up security in Dhaka and more than 60 other cities and towns to prevent violence during the nationwide strike, the AP reports.