TBILISI (Reuters) - Georgia's parliament voted on Wednesday to approve the second reading of a bill on "foreign agents" that has been criticised as Kremlin-inspired, as thousands of protesters opposed to the draft demonstrated on the street outside.

The bill, which would require organisations receiving more than 20% of their funding from abroad to register as agents of foreign influence, has sparked a rolling political crisis in the South Caucasus country, with thousands of protesters taking to the street nightly for almost a month.

Georgian critics have dubbed the bill "the Russian law", claiming it is inspired by laws used to suppress dissent in Vladimir Putin's Russia. Russia is unpopular among many in Georgia, which lost a brief war with Moscow in 2008.

The protests have pitched the ruling Georgian Dream party against a coalition of opposition parties, civil society groups, celebrities and the country's figurehead president, all of whom oppose the bill.

Parliament, controlled by Georgian Dream and its allies, voted along party lines to advance the legislation, prompting a wave of boos from thousands of protesters outside. The bill must pass one more vote in parliament before becoming law.

Late on Tuesday, security forces launched a sudden crack down on protesters outside parliament, using water cannon, tear gas and stun grenades. Sixty-three people were arrested and six police officers injured, Deputy Interior Minister Aleksandre Darakhvelidze said.

The European Union, which gave Georgia candidate member status in December but has said the bill could halt its integration into the bloc, denounced the crackdown as unwarranted.

Wednesday's parliamentary debate was tense, with opposition members expelled and scuffles between legislators, a not uncommon occurrence in Georgia's often-rowdy parliament.

One pro-government deputy was seen throwing a book at opposition legislators, while others shouted and physically confronted opponents.

Levan Khabeishvili, leader of the United National Movement party, Georgia's largest opposition bloc, spoke in parliament on Wednesday with his face heavily bandaged. His party said he was badly beaten by police at the protest, leaving him with concussion, broken facial bones, and missing four teeth.

Supporters of the bill, including Bidzina Ivanishvili, the billionaire founder of the ruling Georgian Dream party and former prime minister, say the foreign agent law would bolster national sovereignty amid what he said were Western attempts to lead Georgia into a confrontation with Russia.

(Reporting by Felix Light, Writing by Maxim Rodionov, Editing by Guy Faulconbridge and Timothy Heritage, William Maclean)

By Felix Light