The current price tag for the Sochi Games is 1.5 trillion rubles ($51 billion), which would make them the most expensive games in the history of the Olympics—more costly even than the much-larger Summer Olympics held in London and Beijing.
The games at the Black Sea resort of Sochi are considered a matter of national pride and one of Putin's top priorities.
The Russian president's decision came after he scolded officials over a two-year delay and huge cost overruns in the construction of the Sochi ski jump facilities.
During his tour of Olympic venues, Putin fumed when he heard that the cost of the ski jump had soared from 1.2 billion rubles ($40 million) to 8 billion rubles ($265 million) and that the project was behind schedule.
"So a vice president of the Olympic Committee is dragging down the entire construction? Well done! You are doing a good job," Putin said Wednesday, seething with sarcasm.
Deputy Prime Minister Dmitry Kozak told reporters Thursday that Putin had recommended that the Russian Olympic Committee fire Bilalov, one of its six vice presidents.
"As far as Bilalov is concerned the president voiced his decision yesterday: People who don't make good on their obligations at such a scale cannot head the Olympic movement in our country," he said.
The Russian Olympic Committee said in a statement that a decision on Bilalov would be made by the executive committee in the near future, a move likely to be only a formality. Putin's power in Russia is such that resisting the call for his dismissal would be almost unthinkable.
Kozak underscored that by saying, "I very much hope that our Olympic movement will listen to the recommendations of the country's leadership."
Most countries that host the Olympics use public funds to pay for most of the construction of the sports venues and new infrastructure such as roads and trains. The Russian government, however, has gotten state-controlled companies and tycoons to foot more than half of the bill.
Both the companies and the tycoons understand the importance of maintaining good relations with Putin, who has a lot of prestige riding on the success of the Sochi games.
Kozak said the costs constantly increased for the ski jump project because Bilalov's company did not properly check the land and, as a result, picked a geologically challenging plot.
"His calculations failed," Kozak said.
Despite these setbacks, Russian officials on Thursday went to great lengths to reiterate that everything in Sochi was now on schedule.
"As (International Olympic Committee) members and we stated yesterday, it is already clear that we have succeeded with this immense—and possibly the most immense—project in Russia's modern history," Kozak said.
Taking a cue from Putin, however, Russian officials sought to play down the high costs. Kozak said the government spent no more than 100 billion rubles ($3 billion) on the Olympic venues and the immediate infrastructure.
The government has spent a total of $13 billion so far, and expects to spend about $18 billion overall before the games begin, Kozak has said previously.
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.