Zia, chief of the Bangladeshi Nationlist Party (BNP), called on her arch enemy and current Prime Minister Sheikh Hasina to hold an immediate dialogue and decide on the mode of the election-time government.
The 68-year-old leader urged thousands of her supporters rallying in the capital to stage street protests demanding fresh polls under a neutral caretaker government.
Zia, a two-time former premier, branded the Hasina government as "illegal" and said: "The government does not have public support. It is trying to stay in power by using force."
"This government is illegal. Hold polls very quickly and test your popularity," she told the rally in the capital's Suhrawardy Udyan park attended by an estimated 35,000 people.
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Zia was placed under virtual house arrest for more than two weeks before the elections, with police laying a siege around her house in a Dhaka neighbourhood.
The BNP chief was prevented from addressing rallies as the government feared it could lead to unrest before the controversial polls. Authorities have officially denied that Zia was ever under house arrest.
She alleged that the government was creating new issues to distract people from other issues.
This was Zia's second public address since October 25 last year, when she issued a 48-hour ultimatum to Hasina to meet the opposition's demand for holding polls under a non-party caretaker government.
Despite the opposition's boycott, Hasina has insisted that her poll victory is legitimate. Nearly 30 people were killed in the deadliest election violence in the country's history.