Around 300 people were injured in the clashes, including some with bullets, the country’s leading Bengali-language daily newspaper Prothom Alo reported.
It added that police had opened fire on supporters of the Bangladesh Nationalist Party, which is led by former Prime Minister Khaleda Zia.
The United News of Bangladesh agency said as many as 150 people including police officers were hurt in the clashes, which occurred in the town of Habiganj.
GK Gaus, a local leader in Ms Zia’s party, said chaos broke out after thousands of party supporters began marching through the streets. Police confronted them and ordered them to stop.
Palash Ranjan Dey, a police official in the district of Habiganj, said police were forced to take action after opposition activists suddenly attacked them while trying to break a police barricade.
Ms Zia’s party has been demanding the resignation of Prime Minister Sheikh Hasina and the transfer of power to a non-party caretaker government until the next general election.
Ms Zia’s party and its allies accuse Ms Hasina of vote rigging in 2018 and the party has been protesting over who should oversee the next general election.
Ms Hasina hopes to return to power for a fourth consecutive term and says the election should be held under her government’s supervision as specified in the constitution.
The United States, the European Union and the United Nations have been urging all sides to avoid violence and work towards holding a credible election.