Brazilian President Luiz Inacio Lula da Silva is in Moscow for talks on boosting trade and investment with Russia.
Brazil and Russia, along with India and China, are members of the BRIC group of economies seeking to increase their economic and political weight.
During talks with Russian leaders, Lula is also expected to discuss Iran, where he will be heading after his Moscow visit.
Brazil, currently one of the 15 UN Security Council members, has publicly opposed a push by Western powers for new sanctions against Iran over its controversial nuclear program and has been seeking to help resolve the dispute through negotiations.
Medvedev said at a news conference with Lula that he expects the Brazilian president's mission will bear fruit.
"I very much hope that the mission of the president of Brazil will end successfully," Medvedev said. "This may be the last opportunity before adopting of certain measures within the UN Security Council."
Until recently, Russia has also been reluctant to discuss sanctions.
compiled from agency reports