Police fired rubber bullets and tear gas at demonstrators in the northwestern city of Rajshahi, while minor clashes erupted in the capital Dhaka and several major towns.
"Up to 500 protesters pelted stones and petrol bombs. We fired rubber bullets and tear gas to disperse them," deputy commissioner of Rajshahi police Shah Golam Mahmud told AFP.
Schools, businesses and private offices were closed across the country and most roads were empty, with thousands of officers on patrol to try to prevent a repeat of violence on Sunday during a similar strike.
The main opposition Bangladesh Nationalist Party (BNP) and its allies called the latest protest as they stepped up demands for elections to be held under a neutral caretaker government.
The caretaker system, under which a non-partisan administration takes over power to oversee national elections, has been scrapped by the incumbent government led by the Awami League party.
On Monday night more than a dozen vehicles were torched or damaged after police arrested the deputy chief of the BNP, Fakhrul Islam Alamgir, on charges of violence during Sunday's strike.
At least two people were killed and dozens were injured Sunday after police and Awami party activists clashed with opposition protesters.
Local television stations ran footage of ruling party supporters attacking a young tailor in front of a courthouse. He died as he was rushed to hospital.
Bangladesh, where the next general election is due in January 2014, has a record of violent politics with rival party supporters often involved in street-fighting.
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Anarchy will rule in all Islamic countries.