TBILISI/BRUSSELS (Reuters) -The European Union urged Georgia on Wednesday to withdraw its controversial "foreign agents" law and warned that the measure would set back the country's ambitions to join the bloc.

Georgia's parliament on Tuesday passed the third and final reading of the bill, which would require organisations receiving more than 20% of their funding from abroad to register as agents of foreign influence, imposing onerous disclosure requirements and punitive fines for violations.

Georgia's opposition parties called for fresh protests on Wednesday, the latest in a series of near-nightly rallies that have sparked a spiraling political crisis in the South Caucasus country.

"The adoption of this law negatively impacts Georgia's progress on the EU path," said a statement from EU foreign policy chief Josep Borrell and the European Commission, the bloc's executive body.

"The choice on the way forward is in Georgia's hands. We urge the Georgian authorities to withdraw the law."

The Georgian government has said the law is necessary to ensure the transparency of foreign funding for NGOs. It did not immediately say if it would back off from passing the bill following the EU's comments.

Bidzina Ivanishvili, an ex-prime minister and one of Georgia's most influential men, 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.

A NATO spokesperson warned on Wednesday that the draft law was a step in the wrong direction for Georgia and would draw it further away from European and Euro-Atlantic integration.

Georgian President Salome Zourabichvili has vowed to veto the bill, telling a joint press conference on Wednesday of foreign ministers from Latvia, Lithuania, Estonia and Iceland that voting for the legislation would "betray the spirit" of Georgia, according to comments cited by Georgian media.

The EU statement said the bloc had "clearly and repeatedly stated that the spirit and content of the law are not in line with EU core norms and values".

Although it did not explicitly say so, the statement made clear that there could be no prospect of Georgia advancing on its path towards EU membership if the law is in force.

EU leaders agreed in December to grant Georgia the status of a membership candidate on the understanding that it completes nine steps, including reducing political polarisation. Diplomats said the bill clearly did not fit with that aim.

The European Commission said the bill would "undermine the work of civil society and independent media while freedom of association and freedom of expression are fundamental rights at the core of Georgia's commitments" to the EU.

The statement followed days of wrangling between EU member governments and officials.

Officials initially tried to agree a statement among the bloc's 27 member governments but that foundered on resistance from Hungary and Slovakia, diplomats said.

It then took more time to agree a Commission statement between Borrell, a Spanish social democrat, and Varhelyi, a Hungarian nominated by his country's nationalist government.

(Reporting by Andrew Gray and Benoit Van Overstraeten; Writing by Lucy Papachristou; Editing by Alexandra Hudson)

By Andrew Gray and Felix Light