The opposition says Hasina's government is not capable of holding a credible election, and it wants a neutral caretaker administration from outside the political parties to oversee the vote.
Hasina has agreed to form a caretaker government, but only with members of the ruling and opposition parties.
One person was killed Monday when police opened fire to break up clashes between ruling and opposition party supporters in Lalmonirhat, 255 kilometers (160 miles) north of Dhaka, the Prothom Alo newspaper reported.
Police in the area could not immediately be reached for comment.
A 32-year-old man died in Dhaka on Monday, a day after his vehicle was attacked with homemade bombs in a Dhaka suburb, a doctor at Dhaka Medical College Hospital said.
Violence on the eve of general strikes is common in Bangladesh, which has a history of violent street protests.
Scores of others were injured Monday in clashes across the country, television stations reported.
An AP cameraman saw protesters throwing homemade bombs at a moving bus as police fired tear gas. Some protesters chanted slogans as they were chased by police. A group of opposition lawmakers chanted anti-government slogans as a van burned on the street.
In addition to the election-related violence, a war crimes tribunal stemming from Bangladesh's 1971 war of independence from Pakistan has become another incendiary political issue.
Hasina formed the tribunal in 2010. Most of those facing trial are members of Jamaat-e-Islami, an Islamic party allied to the opposition. Zia says the trial is politically motivated to weaken the opposition.
On Sunday, the tribunal sentenced two Bangladeshis to death in absentia for crimes against humanity during the war. Bangladesh says Pakistani soldiers and local collaborators killed 3 million people and raped 200,000 women during the 1971 war.
Chowdhury Mueen Uddin, who lives in Britain, and Ashrafuzzaman Khan, who lives in New York, were found guilty of abducting and murdering 18 people in December 1971. The two were among the top leaders of the student wing of Jamaat-e-Islami at the time.