The development comes as there has been no headway in a series of high-profile brutal killings that have rocked Bangladesh.
"Dhaka Metropolitan Police seeks cooperation of the people of the country in tracking them down," said a police statement issued along with the names and photographs of six suspected Ansarullah Bangla Team (ABT) operatives.
The police statement declared a bounty of Taka 500,000 (USD 6,359) for two ABT organisers and Taka 200,000 each (USD 2,544) for four operatives of the banned militant outfit.
ABT earlier claimed to have carried out most of the deadly attacks on secular bloggers, writers, university professors and a gay rights activist, identifying itself as the Bangladesh affiliate of the Islamist State (ISIS).
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Bangladesh authorities, however, have rejected reports of presence any foreign Islamist outfits like the ISIS or al-Qaeda in the country, attributing the deadly attacks on homegrown militant outfits like ABT and Jamaatul Mujahideen (JMB).
The bounty was declared shortly after Prime Minster Sheikh Hasina, now on a visit to Bulgaria, vowed to bring the perpetrators of recent secret killings to the justice.
The Muslim-majority Bangladesh has been witnessing a series of brutal attacks over the past year in which atheist bloggers, academics, religious minorities and foreign aid workers have been killed.
In the latest attack, an elderly Buddhist monk was found hacked to death on Saturday at a temple in a remote hilly region of southeastern Bandarban.
Police last week arrested a suspected ABT militant over the brutal killings of gay rights activist Xulhaz Mannan and his friend Mahbub Tonoy in April.