Medvedev thanks Blatter for choosing Russia
"Russia will stage the World Cup at the highest possible level," Medvedev was quoted by the official Kremlin website as telling the FIFA president.
"The (2018) tournament will be a clear indication of FIFA's new philosophy - to develop football around the world."
Blatter, in turn, thanked Medvedev for his interest in the world's most popular sport, saying Thursday's vote in Zurich had clearly followed the policy of FIFA's executive board.
"(Russia's win) is a great achievement and FIFA looks forward to full cooperation with Russian partners in organising the World Cup," the Kremlin website quoted Blatter as saying.
FIFA's decision to award the 2018 and 2022 World Cups to Russia and Qatar respectively has received a mixed reaction around the world, with some making accusations of corruption within football's governing body.
Russian Prime Minister Vladimir Putin rejected the allegations during his media conference in Zurich on Thursday, saying Russia "won a tough and fair fight".