Frustration with the Russian political system intensified after the ruling United Russia party, led by Medvedev, secured its dominance during last year's elections. Russian President Vladimir Putin's re-election to a third non-consecutive term in office early this year heightened tensions further.
Medvedev was quoted by state-run news agency RIA Novsoti as telling Finnish media that it was "a positive thing" that civil society in Russian "has become more active."
"Certain issues that are being voiced (by the opposition) are probably reasonable and the authorities should take action on them," he was quoted as saying.
Several opposition supporters have been detained in the country, however. Sergei Udaltsov, leader of the opposition Left Front movement, is under investigation for allegedly discussing revolutionary ambitions with political leaders in Georgia.
Putin this week signed a measure that expands the definition of treason to include activity that poses a threat to Russia's "constitutional order, sovereignty and territorial and state integrity."