BRUSSELS (Reuters) - The European Union will downgrade political contacts with Georgia and consider freezing financial aid to the government after it pushed through a controversial "foreign agent" law, EU foreign policy chief Josep Borrell said on Monday.

Speaking after a meeting of the bloc's foreign ministers in Luxembourg, Borrell said the Georgian government was moving the South Caucasus country away from the EU, which it officially aspires to join.

"If the government will not change the course of action, Georgia will not progress on the European Union path," he said.

"We will downgrade our political contacts ... We will consider putting on hold financial assistance to the government," he told reporters.

Borrell said the EU would increase its support to civil society and media and "adapt measures" as necessary. He said the EU would also reconsider its support for Georgia through a military aid fund, the European Peace Facility.

The Georgian law, which requires organisations receiving more than 20% of their funding from overseas to register as "agents of foreign influence", has been slammed by domestic and international critics as a Kremlin-style authoritarian move.

Georgia's ruling party has defended it as a necessary step to secure transparency of funding.

Borrell said 26 of the EU's 27 members shared the view that the government was moving Georgia away from the EU.

He did not name the dissenter but diplomats said it was Hungary. Budapest has tried to clamp down on foreign funding of NGOs and political actors at home and maintains warm ties with Russia, which seeks to maintain influence in Georgia.

For two months, the Georgian bill's opponents mounted some of the largest protests since independence from Moscow in 1991 to try to get the legislation thrown out.

"We stand with the Georgian people and their overwhelming choice in favour of democracy and Georgia's future inside the European Union," Borrell said.

(Reporting and writing by Andrew Gray and Benoit Van Overstraeten; Editing by Sudip Kar-Gupta and Tomasz Janowski)