Russian President Vladimir Putin met with the Pope for the first time Tuesday in the Vatican.
The meeting was expected to help improve relations between the Catholic and Orthodox Churches, which have been strained over the Russian Orthodox Church accusing the Vatican of trying to spread the influence of Catholicism.
"I don't rule out that following the Russian president's visit to the Vatican, Patriarch Alexy II and Pope Benedict XVI could meet soon," Leonid Slutsky, the first deputy head of the State Duma Committee on International Affairs, told journalists.
He said Christian churches should be united in the face of new challenges and threats.
Bishop Ilarion, a representative of the Russian Orthodox Church at European international organizations, said earlier in March that the two Churches have intensified cultural links, but have still not worked out a common position on the problems of Uniatism and Proselytism.
"We need to reach some progress in the discussion of these issues before speaking about any real improvement in relations," he said.
Uniatism is the union of Orthodox Christian communities with Rome through their acknowledgement of the Pope's universal primacy. These Orthodox communities are subject to papal authority, but follow their own Orthodox rites in worship.
The Catholic Church considers only these communities truly Orthodox.
The Russian Orthodox Church also accuses the Vatican of Proselytism, mainly in Western Ukraine, and attempts to convert Orthodox believers into the Catholic religion.
The Catholic Church claims that it is supporting the existing Catholic community and is not proselytizing.