Led by Shipping Minister Shajahan Khan, the 5,000-strong Awami League supporters protested near Zia's office in the capital's posh diplomatic enclave.
Khan asked the government to close Zia's office in Gulshan area, where the BNP chairperson has been staying since January 5 after she was barred from her party's anti-government rally.
"Khaleda Zia is hatching conspiracy in the name of politics at her office. So, we demand that the government immediately close her office down," Khan said.
Khan said if Zia is not arrested, the people will arrest her and send her to jail. "We will return here if she is not arrested."
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He demanded immediate withdrawal of the shutdowns and blockade that has hit the Bangaldesh economy hard.
Finance Minister Abul Maal Abdul Muhith has earlier this month said that Bangladesh may not meet the 7.2 per cent GDP growth rate target this fiscal due to the political unrest.
"Even in December, I was fully hopeful about reaching 7.2 per cent GDP growth... But now I am highly doubtful about reaching the target," Muhith has said.
The BNP-led 20-party alliance enforced its latest spell of 72-hour countrywide strike yesterday, beside the non-stop nationwide blockade that entered its 42nd day today.
Since January 5, when Bangladesh marked the first anniversary of the controversial polls boycotted by BNP and won by Prime Minister Sheikh Hasina-led Awami Leage, the opposition party and its allies have launched strikes one after another to press its demand for a fresh election under a non-party caretaker government system.
The strike and protests by the opposition alliance have also witnessed spates of violence that has until now claimed more than 100 lives.