"I think the efforts that have been made so far and those being made now to eliminate differences between the two Churches must be crowned with success," Mikhail Kasyanov told reporters.
"The Russian government is trying in every possible way to help eliminate the concerns that still exist on the path towards a rapprochement between the two Churches," Kasyanov said at a joint news conference with Prime Minister Silvio Berlusconi.
Berlusconi said he had requested a meeting with the head of the Russian Orthodox Church, Patriarch Alexiy II, and had discussed possible dates for such a meeting with Russian President Vladimir Putin.
The Vatican is attempting to include a stop by the pope in the Russian city of Kazan, 800 km (500 miles) east of Moscow, when he is on the way to Mongolia in August, Vatican sources said earlier this week.
A stop by the pope in Russia, however brief, would be historic, although he has already visited other countries that made up the former Soviet Union.
The pope has said he wants to visit Moscow but would not want to do so without the blessing of the Russian Orthodox Church. It was not clear if the pope would want to visit Kazan unless the Orthodox Church agreed.
Relations between the Vatican and the Russian Orthodox Church have been severely strained since the fall of the Berlin Wall in 1989.
The Russian Orthodox Church has criticised the Vatican for allegedly using new found freedoms in Russia since the end of communism to poach away believers.
The purpose of a stop by the pope in Kazan, some 800 km (500 miles) east of Moscow, would be to return the icon of Our Lady of Kazan, one of the most venerated icons of the Virgin Mary in the Russian Orthodox Church.
The icon, which dates at least to the 16th century, was stolen in 1904 and was kept in several European cities before winding up at the Vatican.
The pope, who wants to mend ties with the Russian Orthodox Church, has said several times that he would like to return the icon to the Russian people.