Leftist leader Sergei Udaltsov said activists have permission to to rally Saturday on Novy Arbat Street in downtown Moscow to protest the results of the Sunday election, in which Putin, who has been prime minister, was elected president.
Critics allege the results were marred by vote-rigging.
"We want new fair elections to be carried out in Russia so that people could choose power for the country without censorship, violations and frauds," Udaltsov told RIA Novosti.
He said the opposition may go on strike or set up tents to increase visibility.
Putin served as Russia's president between 2000 and 2008 but was unable to run for a third consecutive term due to constitutional restrictions. He than ran again after a four-year interval.