Police in the capital Tbilisi used water cannons and tear gas to try to disperse thousands of protesters, who fear the bill could damage Georgia's hopes for EU membership.
The law, which has the support of the ruling Georgian Dream party, would require all organizations that receive more than 20 percent of their funding from abroad to register as "foreign agents" or face significant fines.
The bill has passed its first parliamentary reading, Georgian media reports.
Critics have said it is reminiscent of a 2012 law in Russia, which has since been used to discourage dissent, writes Reuters.
A large crowd can be seen in photos from Georgia.
Photo: ZURAB KURTSIKIDZE/EPA/TT
The President against the proposal
Georgian President Salomé Zurabishvili, who wants to veto the law if it passes, said she stands with the protesters.
- You represent a free Georgia, a Georgia that sees its future in the West, and that will not let anyone take this future from us, she said in a message recorded in the United States, where she is on an official visit.
"No one needs this law ... anyone who has voted for this law has violated the constitution," she added.
However, Parliament can override her veto.
Two of several protesters who took to the streets.
Photo: Nicolo Vincenzo Malvestuto/AP/TT
Strong protests
At least three petrol bombs, as well as stones, were thrown at police outside parliament on Tuesday.
People affected by police tear gas were treated on the steps outside the parliament building.
- I came here because I know that my country belongs to Europe, but my government doesn't understand that, 30-year-old protester Demetre Shanshiashvili told Reuters.
- We are here to protect our country because we do not want to be part of Russia again, he added.
Some of the protesters carried Georgian, EU and American flags while chanting: "No to the Russian law".