"The decision has been taken in principle. We backed a gambling zone in Sochi," Kozak was quoted by Russian news agencies as saying.
Last week, the Russian parliament approved the creation of gambling zones in Sochi and on the Crimean peninsula, a region recently annexed from Ukraine that has numerous beach resorts.
Ahead of the Sochi Winter Games, Moscow built gleaming new stadiums, hotels and transport infrastructure to transform the Soviet-style resort at a cost of more than $50 billion.
Russia now faces the question of what to do with the new structures.
Kozak said the gambling zone was aimed at "improving the financial models" of Olympic projects that received loans from banks including Russia's largest lender Sberbank.
"We must now do all we can to make these projects turn a profit, so they do not go bankrupt," he said.
In 2009, Russia enacted tough anti-gambling laws that forced casinos to shut down across the country. It permitted just four legal gambling zones in its western, eastern and southern regions.
So far however, only one gambling zone is functioning: Azov City, in the same region as Sochi, but on the shore of the Azov Sea.
Three casinos are currently operating in Azov City, the RIA Novosti news agency reported.
Kozak said that in theory, Russian law would require that Azov City shut down if nearby Sochi also became a gambling zone, but added: "This question is under discussion."