Hasina said after a meeting with the mourning relatives of Ahmed Rajib Haider that the Jamaat-e-Islami party, whose members are suspected in the blogger's murder, had "no right to be in politics in free Bangladesh".
Demonstrations championed by the country's online activists have seen thousands take to the streets for the last two weeks demanding the execution of leaders of the Jamaat-e-Islami party who are on trial for war crimes.
Rival protests by Islamists demanding a halt to the trials of Jamaat leaders including its chief and deputy chief over their role in the 1971 independence war have turned violent across the country, leaving 13 people dead.
Late on Friday Haider, an organizer of the anti-Islamist protests, was hacked to death with a machete near his Dhaka home.
Police have yet to comment on a possible motive, but his brother said Haider was targeted by Jamaat's student wing for his online activities. Fellow blogger Shakil Ahmed said a pro-Jamaat website had last week named Haider as a target.
Hasina visited Haider's home on Saturday and hinted in comments to reporters that she would back a ban for Jamaat.
"Anyone can assume who were behind this," she said, alluding to Jamaat.
"Many claim they are a democratic political party, a democratic force. Now it is proved that they believe in terrorism not democracy, she said.
"We will do to them what is necessary. They have absolutely no right to be in politics in free Bangladesh."
Local police Chief Sirajul Islam told AFP at least 50,000 people attended the funeral.
"We touched his coffin and vowed that we won't leave the protests until the government finds his killers, and bans Jamaat and its student wing Islami Chhatra Shibir," said blogger and protester Mahbubur Rahman.
Clashes between police and Islamists have intensified since last week after a senior Jamaat leader was sentenced to life imprisonment for mass murder.
Jamaat and the main opposition Bangladesh Nationalist Party have said the trials are based on bogus charges and are part of a wider political vendetta.
The government rejects the accusations and says the trials are needed to heal wounds of the nine-month war in which it says three million people were killed, many by pro-Pakistani militia whose members allegedly included Jamaat officials.
The killing on Friday was the second attack in Dhaka against a blogger critical of Islamist groups in less than a month, after the stabbing of a self-styled online "militant atheist" by three unidentified men.
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