TBILISI (Reuters) - Thousands of Georgians marched through the capital, Tbilisi, on Sunday, as protests built against a bill on "foreign agents" that the country's opposition and Western countries have said is authoritarian and Russian-inspired.

Georgia's parliament said it would hold the bill's second reading on Tuesday, with opposition parties and civil society groups calling for mass protests against its expected passage.

If passed, the draft law would require organisations receiving more than 20% of their funding from abroad to register as "foreign agents" or face fines.

Protester Nika Shurgaia said he feared many non-government organisations would be shuttered because of what he called "the Russian law". This label has been adopted by the opposition to compare the bill to a law used to crush dissent in Russia.

"There are hundreds of such NGOs who have done so much good for Georgia and now they face being stigmatised and possibly shut down," Shurgaia said.

The EU and Western countries have warned that the bill could halt Georgia's integration with the EU, which granted Georgia candidate status in December

The bill must pass three readings in parliament to become law, as well as overcome a veto by Georgia's figurehead president, who opposes it.

Groups opposed to the bill have protested nightly outside parliament for over a week, since the legislature, which is controlled by the Georgian Dream ruling party, approved its first reading.

Thousands of student demonstrators have blocked Tbilisi's central Rustaveli Avenue, facing off against riot police.

Opponents of the bill who called the mass protests on Sunday have also called for protests against its second reading on Tuesday. The government has called a demonstration in support of the bill for Monday.

(Reporting by Felix Light in Tbilisi; Editing by Elaine Monaghan and Ros Russell)

By Felix Light