The opposition says the government is not capable of holding a credible vote and has threatened to boycott the election unless a caretaker is appointed from outside of political parties.
Hasina has proposed forming a caretaker government from ruling and opposition parties to supervise the vote.
Bangladesh, a parliamentary democracy, has been alternately ruled by Hasina and Zia since 1991. But the issue of peaceful transfers of power has remained a major challenge.
The latest violence killed four people on Monday alone. A man from the ruling Awami League party was stabbed to death by opposition supporters who tried to stop vehicles from defying the shutdown in the central district of Jamalpur, police said.
A driver died in an attack in the southeastern district of Chittagong, a local leader of the main opposition Bangladesh Nationalist Party was killed in a bomb attack, and a teenager died in clashes between government and opposition activists.
At least 50 people were injured when a train derailed in northern Lalmonirhat district after strike supporters uprooted the rail line, Channel 24 TV station reported.
In Dhaka, opposition supporters torched a ruling party office, while schools and businesses remained closed.