The protests were inspired by what the bill's opponents characterized as a Russian-inspired authoritarian action that would dash the hopes of the small country joining the European Union, according to Reuters.
The Georgian Dream party said in a statement it was going to "unconditionally withdraw the bill we supported, without any reservations," adding that it needed to minimize "confrontation" in society while also dispelling "lies" about the bill that had been circulated by the "radical opposition."
However, there is indication that the protests will continue. A group of opposition leaders suggested that protests would resume at 7 pm (1500GMT), with Giga Lemonjava, a Droa party representative, saying that they were demanding that the ruling party scrap the bill and release all those who were apprehended during the protests, according to Reuters.
The bill would have required all organizations in Georgia receiving more than 20 percent of their financial backing from abroad to register as "foreign agents."
The supposed aim of the bill was to cut off "foreign influence" and "spies" from the Georgian political scene. The bill suggested that all Georgians had the right to know who was specifically funding non-government organizations around the country.
However, opponents of the bill said it was reminiscent of a 2012 Russian law that President Vladimir Putin has used in the past to crush opposition for more than a decade.
The proposed "foreign agent" law was a "Russian law that had to be recalled and should not have gone through parliament under any conditions," Nika Oboladze, a Tbilisi resident, said.
"Those who proposed the law are responsible for all this mess. Because 90 percent of Georgians support European integration and nothing should stop that."
Dmitry Peskov, a Kremlin spokesperson, said that the Russian government was "concerned" about the protests that have transpired, adding that the proposed "foreign agent" law shared no similarities with Russian laws.
Opinion polls consistently characterize the majority of Georgians being favor of joining the European Union and NATO. All major parties in the country, including the Georgian Dream, support this idea.