"We now have a positive tendency - we have moved on from a severe frost to a thaw," Metropolitan Kirill of Smolensk and Kaliningrad told journalists in Moscow.
The Russian Orthodox Church has accused the Vatican of seeking to convert Orthodox Christians to Catholicism in Russia and Ukraine, while the Catholic Church says it merely supports existing Catholic communities.
The Russian church has also protested against the Vatican's decision to raise the status of its apostolic administrations in Russia to the level of dioceses. The Orthodox Church saw the move as the establishment of a parallel church organization on Orthodox canonical territory.
Metropolitan Kirill said he hoped the new head of Russian Catholics, Archbishop Paolo Pezzi, who replaced Tadeusz Kondrusiewicz at the post on Saturday, would "contribute as much as possible to improving relations and overcoming existing difficulties."
Pope Benedict XVI's decision to appoint the Italian to the post was widely seen as a diplomatic step to simplify relations with the Orthodox Church, due to the Moscow Patriarchate's disagreements with Kondrusiewicz.
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Ukraine has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.