TBILISI (Reuters) - Georgian Prime Minister Irakli Kobakhidze vowed on Sunday to push ahead with a law on "foreign agents" that has sparked a political crisis, after opponents of the bill rallied in one of the largest protests seen since independence from the Soviet Union in 1991.

Kobakhidze told a televised briefing that the ruling Georgian Dream party would secure passage of the bill in a third reading this week, and threatened protesters with prosecution if they resort to violence.

Georgia's opposition has called on opponents of the bill to stage on all-night protest outside parliament to prevent lawmakers from entering the building on Monday, when they are due to begin debating the bill's third reading.

The bill requires organisations receiving more than 20% of their funding from abroad to register as agents of foreign influence or face punitive fines.

Western countries and Georgia's opposition denounce it as authoritarian and Russian-inspired. Critics liken it to Russia's 2012 "foreign agent" law, which has been used to hound critics of Vladimir Putin's Kremlin.

The dispute over the bill has come to be seen as key to whether Georgia, which has had traditionally warm relations with the West, continues its push for European Union and NATO membership, or instead builds ties with Russia.

The EU, which granted Georgia candidate status in December, has repeatedly said the bill could jeopardise Tbilisi's further integration with the bloc.

Georgian Dream's founder, billionaire ex-prime minister Bidzina Ivanishvili, said last month that the law was necessary to assert Georgian sovereignty against Western powers which he said wanted to drag the country into a confrontation with Russia.

On Saturday evening, a crowd of protesters braved driving rain to stage the largest protest yet, with several columns of marchers shutting down much of central Tbilisi.

A Reuters estimate, using the Mapchecking crowd counting tool, placed the number of protesters at around 50,000 people.

Some Georgian media and activists have put the crowd size in the hundreds of thousands, citing their own calculations. The ruling party said 18,000 attended, but did not explain its reasoning.

(Reporting by Felix Light and Gleb Stolyarov; Editing by Ron Popeski and David Holmes)