The planned protest comes two days after a peaceful march and rally in St. Petersburg - the first time that a demonstration led by Kasparov and his allies in a major Russian city has ended without police violence or interference.
Police have violently dispersed several of the protests - called Dissenters' Marches - held since December by Kasparov and allies in the Other Russia movement who accuse Putin of stifling democracy ahead of parliamentary and presidential elections in the coming year.
The St. Petersburg march took place as foreign executives attended a business forum in another part of the city, raising speculation that police held off to avoid embarrassment as Russian leaders seek to speed the flow of investment dollars into the thriving economy.
Last month, Kasparov and other activists were detained for hours at a Moscow airport to keep them away from a march in the Volga River city of Samara that coincided with a Russia-European Union summit nearby - a move that drew sharp criticism of Putin from EU leaders over his government's treatment of critics.
At the most recent Moscow protest, in April, police beat demonstrators with truncheons and detained dozens including Kasparov. The following day, police beat demonstrators and bystanders after they left the site of a protest in St. Petersburg.
In Moscow, authorities granted organizers permission to protest in a central square Monday but not to parade down a main street, as they requested, raising the strong possibility of a police crackdown if demonstrators seek to march from the square.
City authorities also stipulated that no more than 500 people could attend the rally, in a square in front of a McDonald's restaurant and across the main Tverskaya Street from a statue of the Russian poet Alexander Pushkin, creating the potential for violence if that number is exceeded.
The same limit was in place for Friday's march and rally in St. Petersburg, but police took no action against a crowd that reached about 1,500.
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