Supporters of top opposition leader Alexei Navalny were among some 2,000 anti-Kremlin protesters.
Several thousand members of the ruling party, Communists and other activists also turned out in the center of Russia's second city, Presstv Reported.
Kremlin-friendly marchers were allowed to rally freely, but police used force to break up the opposition column shortly before it could set off.
More than 60 people were detained in the former imperial capital, including local lawmaker Maksim Reznik, said OVD-Info which tracks opposition arrests.
Police refused to say how many people were detained.
"Incredible," Navalny said on Twitter. "They dispersed a sanctioned march for no good reason."
Lawmaker Reznik posted a picture showing five policemen in riot gear dragging him along the ground. He was later released but called his detention an example of "lawlessness."
Thousands of Communists and members of trade unions also demonstrated in the capital Moscow and across the country, waving red flags, in celebrations harking back to the Soviet era.
More than 100 people were detained across Russia, OVD-Info said.
Popular discontent has been building in Russia over recent years amid controversial pension reforms and falling living standards following numerous rounds of Western sanctions over Ukraine and other crises.