It also condemned widespread violations by Syrian government forces in the 18-month-old conflict.
The 47-member Geneva forum adopted a resolution submitted by Arab states by a vote of 41 states in favour, with three states – China, Cuba and Russia – against and three abstentions.
Syria's ambassador Faysal Khabbaz Hamoui rejected the text as "highly-politicised and selective".
Since it was set up a year ago, the inquiry led by Brazilian Paulo Pinheiro has interviewed more than 1100 victims, refugees and defectors, but has been denied access to Syria.
US ambassador Eileen Chamberlain Donahoe told the council: "The work of the commission of inquiry is important because as they continue to document the names of individuals responsible for these crimes and violations."
Switzerland also proposed that Carla del Ponte, a former chief prosecutor of the International Criminal Court, join the inquiry as a commissioner.