Deputies, elected in the 27 Novembervote, will elect speakers of parliament's two chambers, the People's Assembly lower chamber and the Council of the Republic upper chamber.
With 33 seats, the Kremlin-backed Unified Russia party won more than any other party in the 58-seat parliament.
Chechen separatist rebels took no part in the election, calling it a farce. Russian and international human rights groups criticized the polls, calling them a pretense of a political process in the restive republic.
There were few international observers at the election.