"About 20,000 people are attending the event on Academician Sakharov Avenue", the Moscow police said in a statement.
The police added that there were no violations of public order during the demonstration.
Earlier in the day, the police said that it was notified by the organisers of the rally about the provocations planned by opposition figures at the demonstration.
The protests have been going on since mid-July in the Russian capital. They were hosted by opposition figures who were denied registration for the elections to the Moscow city council scheduled for 8 September.
The previous rallies were unauthorized by the Moscow authorities. The protests resulted in the detentions of hundreds of protesters. Most of them were released later. Some of the organizers of the protest were arrested till late September.
