"She (Zia) is playing ducks and drakes with peoples' lives ...This will not be tolerated in any way and she must get her due punishment," Hasina said.
"It is a matter of time. Begum Zia will not only face the corruption charges, she will have to face charges of killings for giving directives," she said during a huge rally in Dhaka.
The rally marked the anniversary of the historic March 7 address of Bangladesh's founder and Hasina's father Sheikh Mujibur Rahman in 1971 which set the course of the country's Liberation War.
The political unrest over the past two months have claimed at least 115 lives.
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Hasina accused Zia of deliberate murders of 55 bus and truck drivers killed during the recent political violence.
She charged Zia of creating instability as part of her "desperate efforts" to grab power. She, however, asked people to resist the violence and sabotage the campaign the BNP-led alliance is carrying out.
Meanwhile, Zia-led BNP and its allies have stepped up their campaign calling for a fresh 72-hour nationwide strike from tomorrow.
BNP now demands a mideterm election under a neutral caretaker government. The general elections are scheduled for 2019.
Traffic in most parts Dhaka appeared standstill for hours as the ruling Awami League mobilised huge supporters in a an apparent show of support it enjoys.
The March 7 address was Mujibur Rahman's last public address ahead of Bangladesh's independence.