The 25-year-old militant was killed during a gun battle with police in northern Bogra district, where he was suspected of bombing a minority Shia shrine last year, the officer said.
Christian hacked to death in latest Bangladesh attack: police
Kawser, who uses one name, was the fourth member of the local Jamayetul Mujahideen Bangladesh (JMB) killed since the crackdown on Tuesday. The banned group is blamed for dozens of murders of religious minorities and secular and liberal activists.
"Kawser was shot during a gunfight between police and JMB militants under a bridge at Shibganj in Bogra," Bogra district police spokesman Gaziur Rahman told AFP. "He died on the way to a hospital."
"He directly took part in the bomb attack on a Shia mosque in Bogra last October and we believe he also took part in other killing missions," Rahman said.
Hindu priest slaughtered in western Bangladesh: police
Three "high-ranking" members of JMB were shot dead on Tuesday during raids by police in Dhaka and in a northwestern district, officers have said.
Bangladeshi authorities have been coming under mounting international pressure to end the string of attacks that have left nearly 50 people killed in the last three years.
In the past four days, an elderly Hindu priest, a Christian grocer and the wife of a top anti-terror police officer have been shot or hacked to death with machetes.
Authorities have blamed homegrown radicals for the attacks, rejecting claims of responsibility from the Islamic State (IS) group and a South Asian branch of al Qaeda.
Suspected militants kill Bangladesh police officer's wife
The killings across officially secular but majority Sunni Muslim Bangladesh have surged in recent weeks and include the murder of two gay rights activists.
Experts say a ban on Bangladesh's largest religious party Jamaat-e-Islami following a protracted political crisis has pushed many towards extremism.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ