On Thursday, Kozak said it was unfair to compare Sochi's budget to that of previous Olympic games because Russian organizers had to build most of the vital and costly infrastructure that was needed — roads, railways, tunnels, gas pipelines — from scratch.
No Russian officials went near the topic of possible corruption, even though Russian business is notoriously plagued by it. Russia last year ranked 133rd out of 176 in Transparency International's Corruption Perception Index, along with countries such as Kazakhstan, Iran and Honduras.
Although there were no documented cases of corruption directly linked to Olympic construction in Sochi, a dozen officials from the Sochi government have been slapped with charges of corruption in the past year.
Kozak and Sochi officials insist that they're keeping the situation under control and that no money is being stolen at Olympic sites.
Sochi organizers also sought to assuage fears that the 2014 Games may fall victim to a warm and snowless winter — or a howling blizzard.
Temperatures at Sochi's Krasnaya Polyana ski resort hovered at 59 degrees Fahrenheit (15 degrees Celsius) on Thursday, and reached 66 degrees F (19 C) in the coastal city of Sochi. That's after a cold snap the previous week in which athletes competed in test events amid snowstorms as temperatures dipped to 20 degrees F (-6 C).
Dmitry Chernyshenko, head of the local organizing committee, said Sochi boasts one of Europe's largest snow-making systems and also has equipment that can store snow throughout the summer and protect slopes and tracks from rain and fog. More than 400 snow-making generators will be deployed on the slopes.
He said Sochi has special equipment that can make snow even in temperatures up to 59 degrees (15 C).
"Snow will be guaranteed in 2014," Chernyshenko declared.
Warm temperatures and rain disrupted some of the snowboarding and freestyle skiing events at the 2010 Winter Games in Vancouver.
The countdown celebrations culminated later Thursday in a star-studded ice show at one of the Olympic arenas, attended by Putin and IOC President Jacques Rogge.
"Today we have come to an important line — exactly a year remains until the first Winter Games in the history of Russia," Putin said at the show. "International test events have shown that the Olympic facilities of Sochi are already prepared to hold the games."
Also Thursday, tickets for the games went on sale online in Russia.
The prices range from a low of 500 rubles ($17) to a high of 50,000 rubles ($1,700). Organizers said about 40 percent of the tickets would be priced under 3,000 rubles ($100). The total number of tickets put on sale was not disclosed.
In a bid to combat ticket scalping, Sochi organizers said they would limit the number of tickets that can be bought by one person. For the most popular events, such as the opening ceremony and top ice hockey games, the limit would be four tickets per person.
Sochi organizers will also require visitors to apply for a special spectator pass without which they will not be able to access the venues.
The games run from Feb. 7-23, 2014.
Nataliya Vasilyeva contributed to this report from Moscow.