Right-wing and ultranationalist organizers had vowed to go ahead with their rally despite a ban by authorities.
The protesters were seeking to proclaim what they see as the superiority of the Russian people and to protest the encroachment of other ethnic groups.
In St. Petersburg, Russia's second-largest city, police broke up a fight between several hundred far-right activists and antifascists.
Dozens of ultranationalists were reportedly detained.
Russia has seen an increase in hate crime, including killings and violent attacks, against foreigners, Jews, and immigrants from Central Asia and the Caucasus.
Opponents of xenophobia and nationalism had vowed to hold a counterrally to combat the "disease of fascism" that they accused the ultraright of spreading.
(RFE/RL Russian Service, AP, Reuters)