"We are seriously looking into it," said Anisul Huq, Bangladesh's minister for law.
"Unless we are totally sure that this claim ... is authentic, I don't think we will be commenting on it."
According to the jihadist monitoring group SITE
, Al Qaeda in the Indian Subcontinent (AQIS) claims that the movement's Bangladesh branch "carried out an operation to slaughter" Nazimuddin Samad in the nation's capital.
Bangladesh police say the 26-year-old writer and graduate student was ambushed by attackers Wednesday night. The attackers slashed Samad with machetes and shot him before escaping the scene on a motorcycle.
Police tell CNN they have yet to make any arrests in the wake of the murder.
In its statement, al Qaeda accused Samad of being an "enemy of Allah." It lists three of Samad's posts on Facebook going back to 2013 as examples of his insults against Islam.
War against atheism
The group effectively declares war against atheist writers who dare to challenge al Qaeda's strict interpretation of Islam.
It also threatens to target judges, lawyers, engineers and doctors "who don't allow others to follow the rulings of the Islamic Shariah."
Samad is the sixth writer or publisher of atheist material to have been murdered in Dhaka in the past 14 months.
Bangladeshi authorities have previously denied that foreign groups such as al Qaeda or ISIS have taken root in the majority Muslim country.
Instead, it says the murders of secular writers in the capital, as well as a series of deadly attacks against Hindu, Christian and Shi'ite minority groups across the country, are the work of homegrown extremists.
Home Minister Asaduzzaman Khan echoed those sentiments on Saturday. He said the issue is not freedom of expression but tolerance of other religions.
"The bloggers, they should control their writing," he told CNN. "Our country is a secular state... I want to say that people should be careful not to hurt anyone by writing anything -- hurt any religion, any people's beliefs, any religious leaders."
The Bangladeshi government has vowed to bring killers to justice.
Law Minister Huq pointed to the December 2015 death sentence handed down to two men convicted of killing blogger Ahmed Rajib in 2013.
Asked if the government would adopt new measures to protect Bangladesh's embattled community of atheists, Huq said security forces had "intensified protective mechanisms."
Several top government officials insist security forces will provide protection to writers who feel their lives are at risk.
Atheists flee Bangladesh
But members of the besieged "free-thinker" intellectual community in Bangladesh say they do not trust the police, because in recent years authorities prosecuted several writers for "insulting religion" in their published work.
"I have not gone to the police because police actually tried to arrest me in 2013," said one atheist blogger in Bangladesh.
He asked not to be identified, due to the fact that he is on a hit list of 84 atheist writers published by a jihadi group more than a year ago. The blogger is part of a network that has helped at least a dozen colleagues flee Bangladesh.
"This community is shattered," the writer said.
To avoid being murdered, the blogger said he stopped posting comments online, changed his phone number and place of residence and regularly changed his route to and from work.
He said he felt like it was a de facto crime to admit to being an atheist in this majority Muslim country.
"I'm definitely living in fear," the writer said.
In 2015, the freedom of press watchdog organization Committee to Protect Journalists listed Bangladesh as 12th in the world on its Global Impunity Index highlighting countries "where journalists are slain and the killers go free."