The 2014 Winter Games, which open one year from Thursday, are expected to cost $51 billion, making it the most expensive Olympics in history.
Putin toured some of the Olympic venues on Wednesday, a day ahead of festivities marking the one-year countdown. He also met with members of the International Olympic Committee, including Jean-Claude Killy, head of the IOC's co-ordination commission for Sochi.
"Today the experts say that 80 per cent of the work is finished," Killy told Putin through a translator. "Still there is one object that requires more efforts to be concentrated on it: It is the ski jump facility, and you know that."
On a visit to the site, Putin grilled government officials on the delay and the cost overruns. Deputy Prime Minister Dmitry Kozak, who is overseeing preparations for the Olympics, was forced to acknowledge during a lengthy, nationally televised exchange that the cost of building the ski jump facility had soared to 8 billion rubles ($265 million) from 1.2 billion rubles ($40 million).
Kozak also was made to explain that state-controlled Sberbank, Russia's largest bank, had taken over the project in May from a company owned by the vice-president of the Russian Olympic Committee, Akhmed Bilalov.
"So it turns out that the vice-president of the Olympic Committee is dragging out the construction. Well done! You are doing a good job," Putin said sarcastically.
The two ski jumps themselves have been completed, but the rest of the complex is now scheduled for completion in July.
At the end of his tour, Putin told officials and private investors to keep a close eye on expenses.
"The most important thing is that nothing gets stolen and that there be no unjustified hikes in spending," Putin said.
Russian officials have dismissed allegations of corruption linked to the preparations for the games.