Kasper, who is head of the Pontifical Council for Promoting Christian Unity at the Vatican, came to Russia at the invitation of local Catholic bishops. But he also met senior officials in the Russian Orthodox hierarchy and renewed the call of Pope John Paul II for a mending of ties between the two churches.
Kasper's appeal -- as well as his reaffirmation that Russian Orthodoxy is a "true church" whose believers must be respected and not subject to Catholic proselytizing -- was clearly aimed at addressing protests over the Vatican's activities in Russia.
Ever since the Vatican was invited to re-open Catholic churches in Russia after the fall of Communism, Russia's Patriarchate has expressed increasing concern over what many Orthodox priests call the "poaching of souls" by Catholic priests.
The Vatican denies having any policy of trying to convert the Orthodox faithful and says most of its new parishioners were previously nonbelievers.
But Orthodox Patriarch Aleksei II has refused the pope's repeated requests to pay an official visit to Russia, citing -- among other factors -- the Vatican's "aggressive proselytism."
Will Cardinal Kasper's conciliatory statement help dispel suspicions and improve relations? For a view from Moscow, RFE/RL spoke to Deacon Andrei Yurchenko, who in the 1990s served in the external relations department of the Russian Orthodox Church.
Yurchenko says he does not believe words will be enough. He notes the Vatican has, in the past, expressed similar sentiments and faces deep suspicion among the Russian Orthodox hierarchy and parishioners.
"I do not believe these words will be enough to satisfy the segment of the population that is interested in such issues, and which at the same time remains very skeptical about the Vatican's policies toward Russia and its policies toward the Russian Orthodox Church. This is unlikely to satisfy them," Yurchenko said.
Ten centuries have elapsed since the schism of 1054 that created the Roman Catholic and Orthodox branches of Christianity. That is too heavy a legacy to be overcome with a few words.
But the Vatican's relations with the Russian Orthodox Church are burdened with additional historical grievances, as well as a heavy dose of internal politics.
Both sides count a litany of past ills, from the Catholics' subordination of Orthodox churches in Lithuania and Poland in the 17th century to the Russian confiscation of Catholic property in Soviet times and killing of Catholic priests -- to cite just two examples.
But according to Yurchenko, the Patriarchate's present hostility to the pope stems not from theology, but a desire to centralize the Russian Orthodox Church's authority within its own ranks.
"This is all a tempest in a teapot. It's clear there are other motivations and ambitions at work here. The issue is not that Catholicism could gain a solid footing in Russia. I don't think anyone is forecasting this or fears this. But the fact is that within the Russian Orthodox Church, there are centrifugal tendencies and therefore, in order to frighten internal dissidents, there is a propaganda campaign against the alleged active proselytizing of Catholics in Russia," Yurchenko said.
Yurchenko does point out, however, that the Vatican's failure to consult with the Russian Orthodox Church over key issues since 1991 -- such as its decision to establish four dioceses on Russian territory -- fuels suspicion among the Orthodox hierarchy. He counsels greater openness.
Michael Bourdeaux is founder and president of the British-based Keston Institute, a think tank which studies church-state relations in Russia and Eastern Europe.
He tells RFE/RL that from a historical standpoint, the pope merely re-established dioceses in Russia that had existed before the 1917 Bolshevik Revolution. But he does concede that better communication between Moscow and the Vatican would have been desirable.
"Those dioceses existed before the revolution and then they were abolished by Communism, so why should the Vatican not unilaterally claim them back? However, I think there could have been more consultation than there was. I'm surprised by the role, of maybe the non-role of the papal nuncio in Moscow. I don't know what, if anything, transpired -- what he transmitted to the Russian Orthodox Church, to the Moscow Patriarchate about the intention of re-establishing those dioceses. But it was clearly his duty to have done so. Whether or not he did that, I just don't know," Bourdeaux said.
Bourdeaux laments the gulf between the Russian Orthodox and Catholic churches, saying it harms the interests of all Christians.
"My view is definitely that a rapprochement is not only necessary but essential. I think it's a scandal in a world where Christian unity -- or at least the attempt to re-establish Christian unity -- is still proclaimed. It's a real scandal that the Vatican and the Moscow Patriarchate have barely been on speaking terms in recent years. There are ever so many ways in which cooperation would be beneficial to both churches, and I think that is something -- if I may humbly say so -- that both the Vatican and the Moscow Patriarchate have to learn," Bourdeaux said.
Bourdeaux notes that Patriarch Barthlomew -- archbishop of Constantinople and spiritual leader of the world's 300 million Orthodox Christians worldwide -- enjoys cordial relations with the pope. This, he says, proves that understanding between the Vatican and the Moscow Patriarchate can be reached.