The protest is being led by several prominent opposition figures, including Boris Nemtsov, who was arrested and jailed for 15 days following a similar demonstration a month ago.
Nemtsov's arrest drew Western condemnation and mobilized his supporters, who held daily pickets outside the jail where he was being kept.
The demonstrations are held on the last day of every month with 31 days to call attention to the 31st Article of Russia's Constitution, which guarantees freedom of assembly.
The city authorized toay's rally, but it also authorized the rally Dec. 31, during which 68 people were detained.
Hundreds of police surrounded the square.
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