The suspected coordinator Mr Mohammad Sakhawatul Kabir and three others were detained in the capital following raids on January 18, Dhaka Metropolitan Police said in a statement.
During interviews, Kabir admitted the four were planning to collect funds and weapons from sympathisers, and the aim "was to attack important offices of the government and establish a caliphate" or Islamic government in Bangladesh, police said.
"Kabir has been working as the Bangladesh representative and coordinator of the ISIS (Islamic State of Iraq and Syria)," it said, adding that he was trained in Pakistan.
Police did not say whether the four had travelled to or fought in Syria or Iraq where the IS group has captured territory.
It was also unclear whether the four, as well as others in South Asia organising under the IS name, were acting on their own or with support from the extremist group in the Middle East.
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