The bill, which won the support of 345 lawmakers on 20 January, must now be approved by the Federation Council, the upper chamber of parliament, and signed into law by President Vladimir Putin.
The Hungarian government has long demanded the return of the 134 books, which were originally kept in a Calvinist college library in the eastern town of Sarospatak. They were transferred to two Budapest banks during the war for safekeeping, but were seized by victorious Soviet troops in 1945.
The books are currently in Nizhny Novgorod in central Russia.
(RIA Novosti, AP)
World War II: 60 Years On
A microsite devoted to RFE/RL's coverage of the 60th anniversary of the end of World War II in May 2005.