Police picked up Adilur Rahman Khan in front of his residence in the capital late Saturday over allegations the group he works for made false accusations against government forces after a deadly crackdown on a protest in May.
"The arrest of Adil Khan appears to be an attempt to silence one of the Bangladeshi government's most vocal critics prior to national elections," Brad Adams, Asia director at Human Rights Watch said in a statement.
Adams urged Bangladesh's donors to press the government to release Khan.
Odhikar's director, A S M Nasiruddin Elan, said the group did not know what the charges were.
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Home Minister Mohiuddin Khan Alamgir said yesterday that Khan was arrested on "specific charges" but did not elaborate.
Elan said police wanted to question Khan in connection with a May crackdown on a hard-line Islamic group. Opposition parties said the government used excessive force and killed scores of people during the May action.
Odhikar said 61 people died in the crackdown. The government asked the rights group to hand over its report about the killings so it could investigate, but Odhikar refused, citing security concerns for the victims' families.
Khan is known to be close to the main opposition Bangladesh Nationalist Party, headed by former Prime Minister Khaleda Zia.