Police said two men were beaten to death in Buzpur town in southeastern Chittagong district in violence between supporters of the ruling Awami League (AL) party and Bangladesh's largest party, the JI.
In another wave of clashes in the southern district of Khulna, a protester from Jamaat was shot dead after police opened fire at 500 of its supporters during the strike.
The violence is the latest to hit Bangladesh, stemming from a continuing war crimes tribunal at which almost the entire JI leadership is in the dock for crimes committed during the 1971 war against Pakistan.
The latest killings brought the overall death toll from clashes triggered by the trials to 100 since January 21 when the court handed down its first verdicts.
"Two men were beaten to death during the clashes. We could not determine immediately which group they belonged to," Buzpur police chief Angshothowai Marma told AFP.
The clashes between some 1,200 secular AL supporters and several thousands of JI supporters were triggered by rumours that the former were going to attack local Islamic seminaries, Marma said, adding that around 12 people were injured.
JI called Thursday's strike to demand the release of the head of its student wing, Islami Chhatra Shibir. Police in Khulna said they opened fire after coming under attack from protesters.
"Police opened fire after they came under attack from 500 Jamaat supporters," Khulna district police chief Ghulam Rouf Khan told AFP, adding that the protesters fired guns and hurled home-made bombs at police.
"A Jamaat man, hit with a bullet in the chest, died on the way to a hospital," another police officer, Kazi Abu Salek, told AFP.
Some 20 JI supporters were hit with bullets and five police officers were injured in the clashes in Khulna, online newspaper bdnews24.com said.
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The Jamaat is here to stay! Its the AL that is struggling for its existance!
Bangladesh, with its enlightened population is well on its way to lead the muslim world. They were very correct in refusing to allow the muslims from Myanmar. However, I wish that after they finish the Jamat, they start to accommodate the bihari muslims in their country. The biharis have suffered long enough for their support of Pakistan and may be they have now learnt a lesson after Pakistan has dumped them. Their disappointment in Pakistan and the lessons they have learnt may make them loyal citizens of Bangladesh.