Georgia’s Parliament gave final approval on Tuesday to a contentious bill that has plunged the country into a political crisis and threatened to derail the pro-Western aspirations of many Georgians in favor of closer ties with Russia.

The law will require nongovernmental groups and media organizations that receive at least 20 percent of their funding from abroad to register as organizations “pursuing the interests of a foreign power.” The country’s justice ministry will be given broad powers to monitor compliance. Violations could result in fines equivalent to more than $9,000.

The passage of the bill is likely to represent a pivotal moment for Georgia, which has been one of the most pro-Western states to emerge from the collapse of the Soviet Union. The bill has already unsteadied Georgia’s relationship with the United States and the European Union, and it could upset the fragile geopolitics of the Caucasus, a volatile region where the interests of Russia, Turkey, Iran and the West have long come into conflict.

The bill has also set off night after night of protests in the capital, Tbilisi, that have often descended into clashes with the police. Dozens of protesters have been beaten and arrested as the police used pepper spray, tear gas and fists to disperse them.

Lawmakers from the ruling Georgian Dream party on Tuesday voted to override a veto of the bill that was announced on May 18 by President Salome Zourabichvili. Ms. Zourabichvili has been among the most vocal opponents of the law, but her veto was largely symbolic, because the government easily had the votes in Parliament to pass it with a simple majority.