MOSCOW — Among the thousands of Russian voices raised against the Kremlin this month after parliamentary elections widely dismissed as fraudulent, perhaps the most surprising was that of Patriarch Kirill I, the leader of the Russian Orthodox Church, who defended popular protests as a “lawful negative reaction” to corruption.

Always a reliable pillar of support for the government of Prime Minister Vladimir V. Putin and his United Russia Party, the powerful Orthodox Church has been noticeably — to some, shockingly — critical of the elections. Arguably the only major national institution outside the state, the church could potentially play a significant role as the current political and social crisis unfolds.