Rapid Action Battalion (RAB) has detained four people, including the alleged mastermind, in connection with the killing of an Awami League (AL) politician and a college student in the capital's Shahjahanpur.
The identities of the detainees could not be ascertained immediately.
The elite force nabbed the four from different parts of Dhaka on Saturday, said ASP Imran Khan, assistant director (media) at RAB Headquarters.
"A man who tailed AL politician Zahidul Islam Tipu's vehicle is among the detainees," he said.
On the night of 24 March, Tipu, who was on a microbus, and Samia Afrin Priti, a 22-year-old college student, who was returning home on a cycle rickshaw, were killed in firing in front of the Islami Bank Hospital.
Tipu was a former general secretary of the AL Motijheel committee while Priti was a student of Begum Badrunnesa Government College.
Tipu's driver was also injured in the firing.
They were all stuck in a traffic jam in the area when a biker wearing a helmet and a mask appeared from nowhere and fired at them, according to police.
The next day, a case was filed against unidentified people over the double murder.
On 27 March, police arrested Akash, 34, the prime accused in the double murder case from Bogura district. The next day, a Dhaka court placed Akash on seven-day police remand for interrogation.
Then on 31 March, a second suspect was arrested by Dhaka Metropolitan Police detectives from the city's Kamalapur area.