The OSCE said the polls were slanted in favour of pro-Kremlin party United Russia, noting apparent manipulations such as the stuffing of ballot boxes.
But President Dmitry Medvedev said the vote was fair, honest and democratic.
On Monday night, at least 2,000 people protested in central Moscow against PM Vladimir Putin, and demanded honest elections.
The election saw a sharp drop in support for United Russia, ahead of Mr Putin's bid to return to the presidency next March.
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