The Rapid Action Battalion (RAB) arrested Ansarullah Bangla Team's (ABT) chief Abul Bashar and two other members suspecting their links with the killing of bloggers Avijit Roy and Ananta Bijoy Das.
The two other members of the ABT, an extremist grouping which claims to be affiliated to Al-Qaeda's Indian sub-continent chapter, were picked up from Dhaka's Fakirapool area, the elite police unit's spokesperson Maksudul Alam said.
The Bangladesh government banned ABT in May over a series of killings of bloggers.
Bangladeshi-American blogger Roy was hacked to death by a gang wielding machetes on the Dhaka University campus while he was walking with his wife in February.
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Das was killed in May by machete-wielding masked men in Sylhet city.
Four secular bloggers, including Roy and Das, have been hacked to death in Bangladesh since the start of the year, sparking international outrage and protests by secular activists in the country.
The banned outfit is blamed for attacks on atheist bloggers and writers.
The murders of the secular bloggers sparked international concerns. The United States expressed its concern over the killing, while the United Nations called for Bangladeshi authorities to ensure accountability and prevent such violence.