The three were found to be carrying licensed pistols and had come to join the rally as activists of the ruling party, a police officer told PTI.
"We have decided to free them with undertakings as they were carrying licensed pistols. Our investigations found they were community level leaders of Awami League," said sub- inspector Delwar Hossain of Shahbagh police station where the three were detained for hours.
Police and witnesses said no one was injured in the blasts near the scene.
However, five ruling party activists were wounded after attending the rally as suspected BNP activists hurled four homemade bombs on a bus in which they were going back to their home in Nawabganj.
Also Read
The five were admitted to state-run Dhaka Medical Collge Hospital, a witness said.
The rally coincided with the first anniversary of Awami League's installation after the divisive January 5, 2014 polls boycotted by the BNP.
Hasina survived several attempts on her life with the most fatal being the August 21, 2004 grenade attack which she escaped narrowly sustaining permanent hearing impairment.