The deceased Shibir cadre in Chittagong is Jasim Uddin, son of Fazal Karim of Fazur Para village under Sodaha union at Satkania upazila.
Another arrested Shibir activist Mohammad Rafique, 30, son of Abu Syed of Muhuripara in the same union, got injured in the gunfight.
Sub-inspector Najmul Haque of Satkania Police Station, who led the drive, said, a team of police had conducted a raid to arrest the duo, accused in at least 20 cases filed for murder, sabotage and criminal attacks as part of protests against the death sentence to Jamaat leader Delawar Hossain Sayedee in February last year.
When the police reached 2 no bridge on Keranihat-Bandarban road around 11:00am, some 20 Jamaat-Shibir activists opened fire on the law enforcers, Najmul Haque said, adding that police had fired gunshots in response.
All but bullet-hit Jasim and Rafuque fled the scene around 20 minutes after the gunfight, he said.
Police said they had recovered two firearms, eight bullets and sharp weapons from the spot.
The injured duo was taken to Satkania Upazila Health Complex around 12:00 noon. But Medical Officer of the hospital Rakib Hasan referred them to Chittagong Medical College Hospital where they reached around 3:30pm.
The duty doctors in the CMCH declared Jasim dead, while Rafique was undergoing treatment there.
Karim Uddin, Rafique's younger brother, said some plainclothes policemen had picked up Jasim and Rafique, and shot them afterwards.
He admitted that the duo had taken part in demonstrations after Sayedee's conviction last year.
Meanwhile, on information that some carjackers were passing through Satkhira district after hijacking a car of Sanjana Zerin, wife of an army officer stationed at Dhaka Cantonment, police signalled the car to stop at Chaltetola in the town around 12:30am yesterday.
Sensing danger, the carjackers fired five to six shots and hurled three crude bombs at the law enforcers, Inamul Haque, officer-in-charge of Satkhria Sadar Police Station, said, adding that police had fired in retaliation.
After 15 minutes of the gunfight, police arrested bullet-hit Ekramullah Babu, 40, a resident of Sultanpur in the town, and his employee Shahidul Islam of Modhumollardangi area.
Babu died at Satkhira Sadar Hospital around 4:30am, hospital sources said.
Shahidul, now undergoing treatment at the hospital, claimed that Mahbubur Rahman, an acquaintance of Babu, was driving the car, which he claimed to be belonging to one of his relatives now visiting India, to Satkhira town when police asked them to stop.
Police claimed that a Police constable also received minor injuries, and the car was hijacked at Rajanigandha Shopping Tower in the capital around 3:30pm Tuesday.