The breakaway church — which calls itself the Ukrainian Orthodox Greek Catholic Church — issued an appeal to Mr. Putin in December to intervene militarily to restore order and defeat what it scorned as “Euro-sodomitic occupation by Brussels programmed by U.S. agents.”

Religion has played an important role in Ukraine’s political tumult, with rival church hierarchies lining up on opposing sides of the barricades. A longstanding split within the Ukrainian Orthodox Church, the country’s biggest, led its Kyivan Patriarchate to support protesters while its Moscow Patriarchate denounced protesters as extremists and hooligans intent on stealing its relics.

But the rift in the Ukrainian Greek Catholic Church, an institution that recognizes the authority of the Vatican but follows rituals known as Eastern Rites, added a murky new dimension to Ukraine’s clerical feuds and threatened division in a part of the country previously known for its nationalist unity.

As with other fundamentalist groups that have split from long-established churches like the Anglican Church in Britain and the Episcopal Church in the United States, the breakaway Ukrainian outfit is obsessed with homosexuality and with preventing any tolerance of what it views as a grave sin. But theological issues, its critics say, mask a geopolitical agenda that puts it firmly on the side of Russia in opposition to Ukraine’s drawing closer to the Europe.

When the Roman Catholic archbishop of Philadelphia, Charles J. Chaput, issued a statement in January voicing sympathy for pro-Europe protesters in Kiev and expressing alarm that Ukraine had “shifted back toward the Russian orbit,” the breakaway Ukrainian church responded with venom. It denounced him as a heretic and, echoing Russian propaganda, dismissed the protesters as “foreign terrorists” and said their demands for human rights “are in fact nothing else than the promotion of homosexual perversion.”

In April, amid rising tensions in eastern Ukraine, where pro-Russian separatists have seized government buildings in at least 10 towns, the breakaway church issued a “pastoral letter” ahead of Easter that made no reference to the unrest stirred by Russia’s supporters but called instead on “brave individuals” to resist the “negative fruits” of the pro-European protests that ousted Mr. Yanukovych. “The only way for Ukraine to be saved is true repentance!” the letter said. “It must call homosexuality a sin! It must condemn the suicidal system founded on the ideology of homosexuality.”

Headed by a 67-year-old fundamentalist preacher from the Czech Republic, Antonin Dohnal, the sect began a decade ago as a dissident movement within the Ukrainian Greek Catholic Church.