The hydraulic brakes caught fire as soon as the driver pressed them at a station
RAB claims the two were 'miscreants'.
Operations Officer Saiful Islam said a RAB checkpost had asked a private car to stop at Rampura early on Sunday.
"But three men got down from the car and opened fire at the RAB posse provoking an encounter," he claimed.
Two of them, wounded in the skirmish, died on way to the Dhaka Medical College and Hospital.
The car's driver fled during the skirmish.
Two RAB personnel were injured during the shootout, he said.
A pistol and six bullets were recovered from the spot.
Another pistol, two jackets used by detective police, a walkie-talkie and a handcuff were found in the car.
"We believe the two were posing as police detectives to commit crimes," RAB officer Islam clarified.