Enamul Haque, 50, the finance affairs secretary of Kotchandpur upazila Jamaat unit, was killed in Jhenidah while two student activists were killed in Satkhira area.
One of the students was a member of suicide squad of the organisation, while other was the secretary of Debhata upazila unit of Shibir, the student wing of Jamaat-e-Islami, police said.
Three sub-inspectors and three constables were injured in the incidents.
Security forces claimed they retaliated in self-defence leading to the gunfight, the police official said.
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The other incident took place in Kotchandpur upazila when security forces, acting on a tip-off raided the spot.
Sensing the presence of forces, the Jamaat men there fired and hurled bombs forcing them to fire back.
During the 20-minute gunfight, Haque of Chandpara village died on the spot, police said.
Haque was accused in a number of cases filed in connection with recent violence unleashed by the Jamaat activists in Kotchandpur upazila of the district, said Kotchandpur police official Shahjahan Khan.
Prime Minister Sheikh Hasina announced a crackdown on unrest led by the opposition BNP and its ally, the Jamaat, after her victory in the January 5 general election, which was marred by deadly violence and an opposition boycott.
Jamaat, blamed for much of the violence in the run-up to the election, said at least 59 opposition activists and party officials have now been shot dead since December 12 when it says the killings started.
Police insist most of those who died were killed during clashes with security forces who were firing in self-defence.