A youth leader of the ruling Awami League was hacked to death by unidentified persons in Chittagong, police said.
Reports from Cox's Bazar district said two workers of the right-wing Jamaat-e-Islami, a key ally of the main opposition BNP, died when police fired on protesters.
Witnesses said a BNP cadre was killed in clashes between police and protesters in western Magura district. An injured worker of the Awami League died overnight in northern Kishorganj, officials said.
The BNP-led 18-party opposition alliance called the shutdown to press for the restoration of the neutral caretaker government system to oversee the next election. The polls are to be held by January 25, 2014.
Supporters of BNP and Jamaat torched a bus in Manikganj and vandalised at least eight vehicles in Gazipur.
Opposition activists earlier exploded several crude bombs in front of houses of ministers and leaders of the Awami League at midnight in Dhaka. Six persons, including a nine-year-old girl and a police officer, were injured in the blasts.
They also set afire a number of vehicles and clashed with police and rival activists in Dhaka, injuring many people.
Incidents of clashes, explosions and vandalism were also reported from other parts of Bangladesh. At least 24 crude bombs were blasted in Rajshahi, Sylhet, Barisal and Joypurhat, reports said.
Twenty rpt twenty people have been killed in violence linked to political turmoil since Friday.
State media reported that public life in Dhaka remained somewhat normal with many people joining work.