All three were detained and charged under section 57 of the draconian Information Communication and Technology (ICT) Act or its more abusive successor, the Digital Security Act 2018.
"Arresting activists, poets, and lawyers for exercising their right to free speech is straight out of the authoritarian playbook," said Brad Adams, Asia director at Human Rights Watch.
"The Bangladesh government should stop locking up its critics and review the law to ensure it upholds international standards on the right to peaceful expression."
A group of writers, artists and journalists staged a protest in Dhaka's Shahbagh square on May 15, saying they would go on an indefinite strike if Sawpon and Mahmood were not released.
Both Sawpon and Mahmood were granted bail on May 16 but Kaium remains in detention.
The ICT Act was widely criticized for granting police wide-ranging powers to make arrests on broad and vaguely defined grounds for any electronically published content, effectively curbing lawful criticism and dissent.