"Before holding a meeting with the head of the Roman Catholic Church, we will have to overcome all differences, which, unfortunately, still exist," he said at a news conference in Paris.
The Patriarch expressed confidence that cooperation between the two churches will contribute to overcoming the dispute.
He stressed that he sees his visit to France as "another step in improving relations between the Orthodox and Roman Catholic churches and in consolidating traditional Christian values."
"Such cooperation is based on a similar approach by the Orthodox and Roman Catholic churches towards moral, social and family values. We together oppose abortion, euthanasia, same-sex marriages and everything that contradicts the Christian doctrine," Alexy II said.
He said that the two churches have run a number of successful projects as part of their UN activities and collaboration with other international organizations.
After the news conference, the Patriarch will meet with French President Nicolas Sarkozy and conduct a service at the Notre Dame de Paris cathedral.
The head of the Russian Orthodox Church, Patriarch Alexy II, earlier accused the Vatican of trying to win new converts in post-Soviet countries regarded by the Russian Church as historically Orthodox.
