The French-sponsored resolution -- to allow the International Criminal Court to begin investigating and prosecuting alleged war crimes committed during Syria's three-year conflict -- received 13 votes in the 15-member group, though permanent Security Council members could block it with a veto.
The vote came after over 50 member countries of the U.N. General Assembly urged the council to approve the resolution.
The Russian ambassador to the United Nations, Vitaly Churkin, argued Wednesday the resolution would be counterproductive to diplomatic efforts to end the fighting in Syria. The Syrian government, which is not a Security Council member, called it a one-sided attempt by France to intervene in its internal affairs.
Although Syria is not a signatory to the treaty that formed the International Criminal Court, the U.N. Security Council has the authority to authorize the court to investigate and prosecute alleged war crimes and other atrocities in countries that have not signed the treaty.