A senior Vatican envoy has ruled out the possibility of a papal visit to Russia for the time being.
Cardinal Kasper admits that mistakes may have been made
But at the end of his trip to Moscow, Cardinal Walter Kasper told journalists he was hopeful "the visit will eventually take place".
Cardinal Kasper, the most senior Vatican representative to have visited Russia for four years, said dialogue "will continue step by step".
His five-day mission was to try to ease tensions between the two churches.
Pope John Paul II's wish to visit Russia has the backing of President Putin but is opposed by Orthodox church leader Patriarch Alexy II.
The Russian Orthodox believe that the pope continues to poach converts in traditional Orthodox territories.
Orthodox lands include Ukraine, where there is an Eastern-rite community of several million Catholics which has been in communion with Rome for over 400 years.
The Ukrainian Catholics, or Greek Catholics, as they are sometimes called, are perceived as a threat by the Orthodox leadership in Moscow.
At a meeting on Sunday, Patriarch Alexey II said that no visit by the pope can be made until these disputes are resolved.
"Proselytism in the territory of Russia and other CIS countries is spreading more and more.
"I am offended by that," Patriarch Alexy told Cardinal Kasper during their meeting.
dismissed the allegations but admitted that there might have been isolated mistakes in the past.
"There may be single cases where wrong behaviour takes place," he told the BBC.
He added that the Vatican might issue stricter instructions to its clergy in Russia, ordering them not to offend Orthodox sentiments.