Hasina also appealed to parents to inform authorities of their missing children after it emerged that most of the hostage-takers in the July 1 Dhaka cafe incident had vanished several months ago.
"Those who are carrying out assaults even in Eid congregations, are enemies of Islam and humanity," said Hasina at an Eid reception at her residence.
"Terrorism will never be tolerated in Bangladesh. The government will do everything to establish peace," she said.
"We will track them down using modern technology, if required they will be given treatment in specialised facilities," she said.
Referring to today's attack before the main Eid prayer, the prime minister said, "They have killed people instead of offering their prayers at time for prayers. How can this be a way to protect Islam?"
"... Those who carry out such heinous crimes, don't believe in Islam in reality. They are the enemies of Islam."
"Steps must be taken against such people who are involved in false preaching and pushing the youths towards death and hell."
She said the Middle East-based militant group had 'gone too far' with their fanaticism regarding Islam. "Islam doesn't allow the killing of innocent people."
Saying the militants had no faith in Allah, Hasina added, "They consider themselves to be more powerful than Allah."
She said, "The international community is with us in the fight against terror. But if anyone from them is backing these militants, the international community itself will have to take responsibility and preventive measures."
She asked everyone to be alert and inform the security
forces about anyone trying to lure the youths towards militancy.
Her appeal to parents came as Bangladesh police and Rapid Action Battalion issued an alert, saying leaving home and joining militants had become a trend among youths.
Bangladesh witnessed a number of Islamists attacks on minorities and secular writers in recent weeks.
Twenty two people, including an Indian girl, were killed last week after suspected Islamic State terrorists stormed a cafe in the diplomatic zone in Dhaka.
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