Monitoring group SITE reported the claim on its website on Thursday.
SITE had earlier published the Middle-East-based militant group’s claims of responsibilities for the murders of Italian aid worker Cesare Tavella in Dhaka and Japanese farmer Kunio Hoshi in Rangpur in past two months.
IS magazine 'DABIQ' claimed it declared Caliphate in Bangladesh in 'Ramadan, 1436' (June, 2015).
It also claimed the responsibilities for the murders of Tavella and Hoshi again alongside the attack on a Shia gathering that left one dead and over 100 injured.
Several Japanese media have also carried out reports on the repeated IS claim of credit for Hoshi's murder.
"These blessed back-to-back attacks have caused havoc among the citizens of the crusader nations and their allies living in Bengal and forced their diplomats, tourists, and expats to limit their movements and live in a constant state of fear," DABIQ said about the attacks.
It said "a new light of hope was born amidst the Muslims of Bengal after the mistakes of the Afghan returnees through the foundation of Jamā’atul Mujāhidīn by Shaikh Abdur Rahman in late 1990s".
It termed the BNP 'nationalist murtaddīn' and its ally Jamaat-e-Islami as 'parliamentary Murtaddīn'
for 'actively taking part in execution of mujāhid scholars' of JMB.
The IS, however, added, "…these same murtaddīn were humiliated, dragged into prison, and given life-sentences and death penalties by the very same tāghūt courts."
It published a photo of Jamaat chief Matiur Rahman Nizami, who has been sentenced to death for the crimes against humanity he committed during the 1971 Liberation War, and called him "the murtadd head of the organisation".