The bill was passed by the State Duma, the lower house of Russia's parliament, on May 8.
The amendments do not set out any specific procedures, but allow the president to introduce a simplified visa regime by decree.
"This decision making mechanism is necessary in situations that require conditions be reworked quickly to successfully implement the country's national interests," Konstantin Surkov, member of the upper chamber's committee for constitutional legislation said.
Surkov added that the bill was needed for events in Russia that involve large numbers of foreign participants, in particular the 2014 Winter Olympic Games to be held in Russia's resort city of Sochi.
The move comes as Moscow prepares for the arrival of over 40,000 English soccer fans for the all-English Champions League final, to be held in the Russian capital on May 21. The Russian Foreign Ministry recently announced that fans in possession of a match ticket would be able to enter the country without a visa for a 72-hour period.
