Four people, including a youth, a truck driver and a ruling party activist, were killed on Monday, police said. The violence began on Friday.
The stand-off between Prime Minister Sheikh Hasina and her arch rival, former premier Begum Khaleda Zia, is nothing new.
The Acting General Secretary of Khaleda's opposition Bangladesh Nationalist Party (BNP), Fakhrul Islam Alamgir, said the government could not be trusted to conduct a credible election.
"Because, in this country, the political parties do not trust each other," he said. "We had the system earlier, but unfortunately this government amended the constitution and brought in the partisan government."
Corruption-plagued Bangladesh is one of the poorest nations on Earth, but the tension is a fresh threat to the garment export industry which has already been rocked by a string of deadly factory accidents over the past year.
Hasina talked with Khaleda by phone on Saturday, but they failed to defuse the crisis. The women have alternated as prime minister for most of the last 22 years, most of the time barely speaking to each other.
Hasina has offered the formation of an all-party government to see through the elections with her staying as head of government.
Bangladesh has already been hit by a wave of violent protests over war crimes convictions and more than 100 people have been killed in protests and counter-protests this year.
