The resolution, supported by 94 of the assembly's 193 members, said that Russia, which invaded Ukraine in late February, "must bear the legal consequences of all of its internationally wrongful acts, including making reparation for the injury, including any damage, caused by such acts," news agencies reported.
Fourteen countries voted against the resolution in New York on Monday, including Russia, China and Iran, while 73 abstained and the rest did not vote, the Reuters news agency reported.
Nearly 50 nations, including Poland, co-sponsored the resolution, which calls for the establishment of an international mechanism for compensation for damage, loss and injury, as well as a register to document evidence and claims, according to the un.org website.
The Ukrainian ambassador to the UN, Sergiy Kyslytsya, told the General Assembly before the vote that his country "will have the daunting task of ... recovering from this war, but that recovery will never be complete without a sense of justice for the victims of the Russian war."
He insisted that Russia must be held accountable for its violations of international law.
Poland's ambassador to the United Nations, Krzysztof Szczerski, appealed to member states to vote in favour of the resolution on "Furtherance of Remedy and Reparation for Aggression Against Ukraine."
Szczerski in a speech called for "the creation of a Register of Damages caused by Russia’s aggression against Ukraine," according to Polish officials.
'Diplomatic victory in New York': Ukraine's Zelensky
Ukrainian President Volodymyr Zelensky in a tweet hailed a "diplomatic victory in New York."
He said: "The UN General Assembly has just given the green light to the creation of a compensation mechanism for Russian crimes in Ukraine. The aggressor will pay for what he did."
The UN General Assembly last month voted overwhelmingly to condemn Russia's attempted annexation of four Ukrainian regions.
Source: PAP, Reuters, un.org
Click on the audio player above for a report by Radio Poland's Michał Owczarek.