Russia is bidding against England, the United States, and combined bids by Spain and Portugal and by Belgium and the Netherlands for the 2018 tournament.
Those same bidders, as well as Qatar, Australia, Japan and South Korea, are also up for 2022.
"If we get the honour (of staging the 2018 finals) we can offer additional government guarantees regarding visa-free entry for participants and guests," Putin told visiting officials from FIFA, football's world governing body.
In April, Putin signed Russia's World Cup guarantees for a wide range of issues including security, tax and customs breaks.
"We will have everything ready on time, using both state and private capital. We would stage (the tournament) at the highest possible level, I have no doubt about it," he said.
