More than a half of the spending, or 336 billion rubles ($10.5) would be allocated from the federal budget, Medvedev told a government meeting Thursday, reports Xinhua.
Noting that the programme was approved under deliberate review, he called on "the most effective and transparent way" to use the money.
The World Cup 2018 "gives one more opportunity to attract private investments, and it is needed to take advantage of it for sure", Medvedev added.
He urged the government "to do everything to form a tourist infrastructure in Russia. Thanks to those investments, which the state authorities and private investments are making".
Medvedev said about one million spectators were expected to attend the World Cup, which will be held in 11 Russian regions.
"Therefore, it is needed to create conditions for a comfortable stay not only of the fans and teams, but also for the studying of Russian culture," the prime minister said.
"The programme envisages the construction and reconstruction of 12 stadiums and 113 training grounds," he added.