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The leaders of the BNP have blamed overcrowding for the mishap, in which several people received minor injuries.
A part of the stage caved in when BNP Health Secretary Fawaz Hossain Shubho was delivering speech at the rally in front of the party's Chittagong office in Nasiman Bhaban in the afternoon.
The BNP's National Standing Committee Member Amir Khosru Mahmud Chowdhury was onstage at the time. He was unharmed.
Chittagong city BNP Vice-President Abu Sufian also blamed overcrowding for the collapse.
Amir Khosru and other leaders of the party and its affiliate delivered speeches after the incident.
Among others, Mohila Dal President Afroza Abbas and General Secretary Sultana Ahmed spoke.