A police official said 13 people, including two police officers and a paramilitary soldier, were killed in clashes in Kanchpur, just outside Dhaka. He said seven others died in a commercial area of the capital.
The protesters blocked roads with burning tyres and logs during more than five hours of clashes. They also attacked a police station and set fire to at least 30 vehicles, including police trucks, television reported.
The United News of Bangladesh reported that the violence erupted after security forces fired tear gas and rubber bullets at protesters in the central commercial district.
Dhaka Metropolitan Police said in a statement that all rallies and protests had been banned in the city until midnight for fear of more clashes.
The Islamist activists have been demanding that the government implement an anti-blasphemy law. The government of the Muslim-majority nation has rejected the demand, insisting that Bangladesh is governed by secular law.
On Sunday, police fired rubber bullets to disperse stone-throwers among thousands who rallied around Dhaka. Officials said at least one person died and 45 were injured. The ruling Awami League and an opposition alliance had both planned rallies later in response to Sunday’s violence but postponed them.