A group of unknown men stabbed a police officer to death on Wednesday just outside the capital Dhaka, while another was badly injured, the second such attack in less than a month.
Police officer stabbed to death in Bangladesh in new attack
Home Minister Asaduzzaman Khan blamed local hardline militants, whom the government also suspects are behind a series of murders this year of secular bloggers and a publisher of secular books.
But the Islamic Stae group (IS) said its "soldiers of the state in Bangladesh" carried out Wednesday's killing, according to the US-based militant monitor group SITE.
"The soldiers of the Caliphate withdrew safely, and unto Allah is all praise and gratitude," IS said in a statement late on Wednesday.
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In recent weeks, IS has also claimed responsibility for murders of an Italian aid worker and a Japanese farmer, along with a blast at the country's main Shia shrine which left two people dead.
If the latest claims are true, it would be the first time IS has targeted an arm of the Bangladesh government.
The government has rejected the terrorist group's previous claims, saying it does not have any presence in the country.
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An al-Qaeda branch has also claimed responsibility for the blogger and publisher attacks, calling the victims "atheists and blasphemers".
The government has instead blamed local militants, along with the main opposition party and its militant ally, for orchestrating the violence to destabilise the country.
Prime Minister Sheikh Hasina's government launched a crackdown on local terrorist groups after facing Western criticism this year of failing to stop the bloodshed.
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