KIEV, Ukraine — Pro-government demonstrators deployed a new tactic on Friday to counter protests in favor of European integration, marching through the capital, Kiev, to oppose homosexuality, which they said would accompany a greater European Union role in Ukrainian affairs.

Carrying religious icons and singing hymns, the group of about a thousand Orthodox Christian supporters of President Viktor F. Yanukovich filed out of a monastery and marched to a city park.

Marchers said they favored allegiance to Russia rather than Europe because Russia more closely matches the cultural and religious heritage of Ukraine, once part of the Soviet Union. They intend to draw attention to what they characterize as overly liberal European social values, they said.

The protesters set off from the Kiev Pechersk Lavra, a monastery controlled by the Moscow Patriarchate, which is subordinate to the Russian Orthodox Church and is one of three denominations of Eastern Orthodoxy in Ukraine. The Kyivan Patriarchate of Ukraine, in contrast, has supported the pro-Europe demonstrators and has allowed many to sleep in churches.