Avijit Roy was hacked to death by two assailants with machetes on the streets of the capital Dhaka in February as he returned from a book fair with his wife.
AQIS leader Asim Umar said his organisation was responsible for the attack in a video posted on jihadist forums yesterday, according to SITE, a US website that monitors extremist groups.
He also claimed the murders of other "blasphemers".
A spokesman for Bangladesh's Rapid Action Battalion (RAB) force, which is tasked with tackling militancy in the Muslim- majority nation, said it couldn't be certain the claim was correct.
Haider and Rahman were also killed by machete-wielding attackers. Haider died in 2013 and Rahman was hacked to death in March.
A little-known Bangladeshi militant group called Ansarullah Bangla Team (ABT) has also apparently claimed responsibility for Roy's murder via a twitter account which police have not been able to verify as genuine.
The Bangladesh-born writer, who emigrated to the southern US state of Georgia some 15 years ago, was well known in his native land for his Mukto-Mona (Free-mind) blog where he railed against all forms of organised religion.
In March, police arrested two madrassa students over the killing of Rahman. Police are investigating whether they belonged to ABT and whether they had any connection with Roy's murder.
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