The men, identified as 'Mosharraf', 40, and Monir Hossain, 35, were injured during the shootout near the Azimpur Chinnamul Market around 4:00pm Tuesday, RAB-10 Commander Shahbuddin Khan told bdnews24.com.
A RAB patrol team had moved to the area after receiving information about a gang of muggers, he said.
The gunfight began when the RAB personnel signalled two private cars - one white and another black – to stop over ‘suspicious movement’.
The white car had a banner that said DMP, the abbreviated form of Dhaka Metropolitan Police, said the RAB-10 official.
“The passengers of the white car began shooting, prompting RAB personnel to fire back. During the brief gunfight, the black car managed to escape.
They men with bullet wounds in their thighs were being treated at the Dhaka Medical College Hospital, he said.
"The members of this gang tell victims they are police detectives to force them inside their vehicles. There are many gangs who use this method to rob people. We are trying to arrest them.”
Two firearms have been recovered from the car now in RAB custody.