Opposition parties took to the streets to protest against the appointment of an interim government headed by a former member of the ruling party on Friday.
At the same time supporters of the ruling party fought street-battles with former members who had defected to set up a new group.
Police said four men were killed in shootings or bomb attacks in the capital Dhaka and other towns.
Two women died after being run over by a speeding bus in the capital's eastern suburbs.
The violence spread across the country after Begum Khaleda Zia, the outgoing prime minister addressed the nation on state television on Friday evening to call for peace when she steps down on Saturday.
Elsewhere in the country, protesters blocked a key highway, cutting road links between the capital and southeastern port city of Chittagong.
Sporadic violence continued through the night in at least a dozen other provincial towns. Police fired teargas and rubber bullets to disperse rioters, witnesses said.
The Awami League, the country's main opposition party, has strongly opposed Zia's plan to install KM Hasan, the former supreme court chief justice, as the head of the interim government.
The Awami League say that Hasan's past association with the ruling party means that he will not be a sufficiently neutral during the run-up to elections in January.
Awami League supporters have said they will take steps to paralyse the country if the government presses ahead with its plan to appoint Hasan as interim ruler.
The government has so far not set a date for Hasan's swearing-in ceremony.