Tens of thousands defied a heavy police presence to join the rallies on Saturday. More than 3,500 were detained, monitors say.
But President Vladimir Putin's spokesman the next day claimed only "a few" people had turned out.
There are calls for the EU to step up sanctions on Russia amid US accusations of "harsh tactics" against protesters.
In Moscow, riot police were seen beating and dragging away demonstrators.
Mr Navalny, President Putin's most high-profile critic, called for protests after his arrest last Sunday.