By David Willey
BBC correspondent in Rome
The Vatican and the Russian Orthodox Church have agreed to set up a joint working group to try to improve relations.
Kasper is trying to smooth relations for the Vatican
The announcement was made simultaneously in Rome and Moscow.
The most senior Vatican representative to visit Russia for four years is currently on a mission to try to mend bridges between the two churches.
Cardinal Walter Kasper is in charge of the Vatican's relations with other Christian Churches.
The aim of his five-day mission: to try to persuade the Russian Orthodox church of Rome's good faith.
The Russian Orthodox believe that Pope John Paul II continues to poach converts in traditional Orthodox territories. The Vatican denies this.
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.
Russian Patriarch Alexy II, who will meet Cardinal Kasper before he returns to Rome, sees the recent Vatican decision to promote the Ukrainian Catholics' leader to the rank of patriarch, and to allow him to move his headquarters from western Ukraine to the capital, Kiev, as a potentially hostile act.
On the eve of the cardinal's arrival, the Moscow patriarchate issued a statement to the effect that the world's 15 Orthodox Churches are unanimous in condemning the Pope's decision.
Under these circumstances, it looks increasingly unlikely that the Pope will ever be able to fulfil his long-held ambition of visiting Russia - almost the only country in the world, apart from China, to which he has been unable to travel during his quarter of a century of worldwide pilgrimages.