The two people were escorted out of the venue at the Suhrawardy Udyan by security agencies after three Molotov cocktails exploded at the venue.
"The two were detained as they were carrying two pistols with 50 bullets," a report by the private 71 television channel quoted a security official as saying.
But police said the two were immediately taken to a nearby police station for initial interrogation and subsequent investigations.
The rally coincided with the first anniversary of Awami League's installation after the divisive January 5, 2014 polls boycotted by the BNP.
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The rally though was organised to mark the Home Coming Day of Bangladesh's founder and Hasina's father Bangabandhu Sheikh Mujibur Rahman from captivity in Pakistan in 1972.
"Adequate security arrangements are there, there is no reason to panic," a police spokesman earlier told newsmen ahead of the rally while the elite Special Security Force (SSF) enforced a tight vigil in an around the venue at central part of the capital.
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.
Twenty four people including the women front chief and former president Zillur Rahman's wife Ivy Rahman were killed in the attack which also crippled over 200 people.