Home Minister Asaduzzaman Khan said the nation's intelligence agencies went straight to work after a gang of machete-armed attackers hacked the blogger to death at his home in the capital on Friday.
"We hope we'll catch the killers soon. They'll be hunted down," the minister told AFP, adding that the killers appeared to have been well-prepared for the assault.
Police confirmed Chakrabarti, 30, was murdered at his home in the capital's Goran neighbourhood by a group of four people who had pretended to look for a place to rent.
Read: Fourth secular blogger hacked to death in Bangladesh
Asha Moni, wife of the slain blogger, later told reporters that one of the men attacked her husband shouting "Allahu Akbar (God is greatest)".
The Bangladesh branch of Al-Qaeda in the Indian Subcontinent (AQIS), Ansar al-Islam, claimed the murder and warned of more to come, according to monitoring group SITE.
Chakrabarti is the fourth secular blogger to be killed in the Muslim-majority nation since February, when Bangladeshi-born US citizen Avijit Roy was hacked to death in Dhaka.
Read: Third secular blogger knifed to death in Bangladesh
The latest killing sparked outrage as hundreds of secular activists joined protests, decrying a culture of impunity in the country.
Amnesty International said the government had to do more to stop "this spate of savage killings", while the US State Department condemned it as a "cowardly murder".
The home minister rejected criticism that his government was not doing enough for the safety of secular writers, adding that it was "trying" to protect hundreds of them.
In a Facebook post on May 15, Chakrabarti said he had been followed by two men after protesting the murder of another blogger, Ananta Bijoy Das, but police refused to register his complaint and instead told him to leave the country.
Read: Another blogger hacked to death in Bangladesh: police
But Khan said the blogger "did not file any general diary (complaint with police)".
Most secular bloggers have gone into hiding, often using pseudonyms in their posts, and at least seven have fled abroad, according to Canada-based atheist blogger Farid Ahmed, who has helped several of them.
Chakrabarti, who used the pen-name Niloy Neel, wrote against Islamic and other religious fundamentalism on a variety of anti-religion websites and blogs.
Bangladesh is officially a secular country, but more than 90 percent of its 160 million people are Muslim.
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