The violence took place as the Jamaat-e-Islami party enforced a day-long general strike across the South Asian nation following last week's execution of Abdul Quader Mollah for war crimes committed during Bangladesh's 1971 independence war against Pakistan.
Three men died of bullet wounds following clashes in Lalmonirhat district in northern Bangladesh, said Praful Kumar, a doctor at a government-run hospital.
Another man died and 15 people were wounded in similar violence between police and Jamaat-e-Islami activists in the northern district of Joypurhat.
The new violence took place amid growing political tensions in the country. At least 24 people have been killed in clashes involving opposition and pro-government activists and police since Mollah was executed on Thursday.
His party says the execution was politically motivated. Authorities said he was tried and convicted according to law.
Bangladesh says Pakistani soldiers, aided by local collaborators including Mollah, killed at least three million people and raped 200,000 women during the nine-month war against Pakistan.
Also yesterday, thousands of businessmen linked hands in the streets of Dhaka, the capital, and other major cities, calling for peace and shunning violence.
They carried white flags symbolising reconciliation. Many of their businesses have suf- fered because of a string of general strikes and blockades enforced by the opposition in recent months.
While Jamaat-e-Islami protested at the execution, many among Bangladesh's 160 million people have praised prime minister Sheikh Hasina for trying and executing Mollah.
Opposition parties are also protesting at the government's decision to move ahead with national elections due to take place on January 5.
The opposition wants the government to resign and hand over power to an independent caretaker to oversee the vote.
Sheikh Hasina has vowed to continue the trials of the war crimes suspects and push ahead with the elections despite calls from opposition leader and former prime minister Khaleda Zia to resign.
Mollah's party is a key ally of Zia's Bangladesh Nationalist Party. Most of those being tried for war crimes are connected to the country's opposition. Jamaat-e-Islami is barred from taking part in next month's elections.
Bangladesh will celebrate the nation's victory day today.
Pakistani soldiers surrendered to a joint Indian-Bangladeshi force on December 16, 1971.
India helped Bangladesh, then the eastern wing of Pakistan, in its fight for independence.