Law enforcement agencies said protesters clashed with police in some areas and with government supporters elsewhere, the BBC reported.
Opposition leaders said Bangladeshi Prime Minister Sheikh Hasina must install a neutral caretaker administration to oversee the general election in January.
Hasina said she want to install a coalition government involving all parties.
Reporters of violence first came from the Faridpur district, about 80 miles from Dhaka. Police said they had to open fire because protesters threw stones at them and blocked a main highway.
Activists said police shot and killed a 22-year-old opposition supporter, the BBC said.
In the town of Ishwardia, a 28-year-old opposition activist was killed in clashes with government supporters, while in Jessore, a government activist reportedly was hacked to death by protesters, the British broadcaster said.
The strike began Sunday with the main opposition Bangladesh Nationalist Party and its Islamist ally Jamaat-e-Islam expressing hope to grind the government to a halt to try to force Hasina to allow a neutral caretaker administration to oversee the election process. The BNP and its allies have said they won't participate in elections under existing constitutional provisions, which don't allow for a neutral caretaker government or require the incumbent prime minister to step aside during the interim.
On Friday, at least six people were killed when security forces fired on opposition supporters defying a ban on protests.