Home Minister Asaduzzaman Khan's statement came days after Ansar al-Islam, the Bangladeshi division of al Qaeda in the Indian Subcontinent, claimed responsibility for the killing of blogger Nazimuddin Samad last week.
Samad's death marks the sixth time a Bangladeshi writer of atheist material has been killed in 14 months.
Khan said the issue is not freedom of expression but tolerance of other religions.
"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," Khan said.
He said that home-grown militants and not the Bangladeshi branch of al Qaeda are responsible for Samad's murder.
Khan said authorities are investigating two to three people in connection with the attack, but have not arrested them because officials are still trying to confirm their involvement.
Bangladeshi authorities have previously denied that foreign terror groups such as al Qaeda or ISIS have taken root in the majority-Muslim country.
Samad, a graduate student, was on his way home from evening classes on Wednesday when three to four people circled him.
"First the attackers hacked Samad with machetes, then shot him," Dhaka Senior Assistant Police Commissioner Nurul Amin had said.
Police said the attackers then fled the scene on motorcycles. No arrests have been made.
In its statement claiming responsibility, al Qaeda accused Samad of being an "enemy of Allah." It listed three of Samad's posts on Facebook going back to 2013 as examples of his insults against Islam.
It has also threatened to target judges, lawyers, engineers and doctors "who don't allow others to follow the rulings of the Islamic Shariah."
The Bangladeshi government has vowed to bring killers to justice.
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, the report said.
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