Bangladesh opposition leader Khaleda Zia urged supporters on Monday to stage fresh protests to try to force new elections, at her first public rally since authorities eased her de facto house arrest.

Zia, a two-time former premier and the arch enemy of current Prime Minister Sheikh Hasina, branded the new government illegal after bloody elections earlier this month that were boycotted by the opposition.

Zia also urged thousands of her supporters rallying in the capital to start a new round of street protests to force Hasina's new government to hold fresh polls under a neutral caretaker government.

"This government is in power because of gun power, not people's vote," she told the rally in the capital's Suhrawardy Udyan park.

"This government is illegal. Hold polls very quickly and test your popularity," she urged it in a speech to the crowd, which police said numbered 35,000.

Zia was placed under virtual house arrest for more than two weeks before the elections, with teams of police standing guard outside her house in a Dhaka neighbourhood -- fearful she would lead rallies and inflame unrest.

She was allowed to leave her home on January 11 to attend a meeting, although authorities have officially denied that she was ever under house arrest.

Hasina has insisted her walkover win in the polls was legitimate, despite a boycott by Zia's opposition Bangladesh Nationalist Party and its allies and the deadliest election violence in the country's history.

At least 26 people were killed during the poll, making it the bloodiest vote in Bangladesh's history, while hundreds of opposition supporters torched or trashed polling stations.

In the weeks before the polls, the opposition staged protests, strikes and transport blockades in a failed bid to have the vote called off. The violence left around 200 people dead.

The Election Commission says voter turnout on January 5 was 40 percent but independent observers and local media said the turnout was not more than 20 percent -- a record low in the nation's short electoral history.

Zia's demand for fresh polls follows similar calls from the United States --- Bangladesh's largest trade partner -- and other nations, who want the government and the opposition to hold talks as soon as possible.

Zia on Monday repeated her claim that the government has engaged in arbitrary arrests, "enforced disappearances" of party leaders and the murder of opposition activists.

The government has since the polls launched a nationwide crackdown on opposition activists, arresting more than one thousand.

About a dozen opposition supporters have been shot dead in alleged encounters with police, according to activists.