Supporters and critics of Russia's president are demonstrating in Moscow, with both groups calling attention to Kremlin plans to consolidate power.
Hundreds of prominent critics of President Vladimir Putin's denounced the legislation as a step back for democracy and an increase in authoritarian rule.
State-run media reported another rally elsewhere in Moscow of 15,000 Putin supporters.
The rallies came on Russia's Constitution Day, as Mr. Putin signed into law a bill letting the president appoint who can run for governor. Another of the president's proposals, aimed at scrapping the direct election of national lawmakers, is also expected to win parliamentary approval.
The Kremlin says the changes are needed to bolster security in the wake of the Beslan school terrorist assault. Hundreds died in the attack, many of them children.