Police said a supporter of the main opposition Bangladesh Nationalist Party (BNP) was hacked to death in the western town of Magura, and scores including a city mayor were injured just outside the capital Dhaka.
A senior police officer was also seriously injured by a small bomb in the capital's Hazaribagh area, during a series of clashes nationwide.
"Hit by seven splinters, the officer was rushed to hospital. He is seriously injured but now out of danger," Maruf Hossain, deputy commissioner of Dhaka police, told AFP.
At least 17 people have been killed since Friday when the opposition began a push to force Prime Minister Sheikh Hasina to quit.
After a series of mass rallies at the weekend, the BNP and its allies enforced a three-day general strike which ends later Tuesday.
But this is unlikely to ease tensions.
A court in Dhaka is due to give its verdict Wednesday on 823 soldiers accused of taking part in a mass mutiny in 2009 soon after Hasina came to power.
BNP leader Khaleda Zia, who has twice served as premier, has long been seen as close to the military. Her husband was a former army chief who became president in 1977 in the aftermath of a coup.
Zia, who has a notoriously toxic relationship with Hasina, has branded the current government "illegal" and says that under the law a neutral caretaker government must be set up three months before national elections, due in January.
Hasina has scrapped the caretaker system and instead proposed an all-party interim government led by herself to oversee the polls.
On Saturday Hasina invited Zia to hold talks and urged her to postpone the strike, during a 40-minute phone conversation believed to be the first time in at least a decade that they have spoken.
But leaked audiotape of the conversation showed they spent most of the time quarrelling over their past records.
"You killed people by carrying out the August 21 grenade attack," Hasina said during the call, referring to blasts at her rally in 2004 which killed at least 20 people and injured Hasina, then the opposition leader.
"We did not do the killing. The longer you live is better for us. The more indecent language you use, the better for us," said Zia.
Hasina also accused Zia of celebrating a fake birthday on August 15, which is also the anniversary of the assassination of Hasina's father who was the country's founding leader, along with almost her entire family.
Zia shouted back: "Can't anybody be born on that day?"
Bangladesh has been ruled alternately by Hasina and Zia since 1991, apart from when a military-backed government ran the country between 2007 and 2008.
Since independence in 1971 the country has seen at least 19 coups although the power of the military has diminished in recent years.
While no senior officers were implicated in the 2009 mutiny, the uprising fuelled the sense that many people serving in the military were opposed to Hasina.
Fifty-seven top army officers were killed in the event.
Lead prosecutor Baharul Islam told AFP that his legal team expects judges to hand down the death penalty on Wednesday against most of the accused, who include a former BNP lawmaker.
While the nation has a long history of political violence, this year has been the deadliest since the former East Pakistan broke away from Islamabad and gained independence.
At least 150 people have been killed since January after a controversial court began handing down death sentences on leaders allied to ex-premier Zia.
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