During the drive to the rink, he explains that he was never able to keep his balance on blades, even as a child; he does not know the reason.
Mr. Putin disappears into a private dressing room, and then graces the ice, his 5-foot-7 frame marked by a national team jersey with “V.V. Putin” on the back and the number 11.
Before the three-on-three match begins, Mr. Fetisov leads the Prime Minister through skating, passing and shooting drills – and is probably the only Russian allowed to bark at the man, as he implores him to carve harder on his turns.
On their mission to stanch the decline of Russian hockey, the two men masterminded the Kontinental Hockey League, Russia's professional league that aims to challenge the NHL. “It was my idea,” Mr. Putin says before launching into an economic argument about the monopolistic behaviour of single-league sports and how they weaken a game by limiting external competition.
It's a curious argument for a man who has centralized parts of Russia's economy, and can direct entire sectors of the economy.
But those who want a two-dimensional view of Mr. Putin tend to be disappointed, just as those are who view Russia as a single place.
In hockey, as in economics and politics, he favours managed competition, with state actors and private enterprise, all under the direction of a benevolent leader, which of course happens to be him.
Using state support and private money, he and Mr. Fetisov have orchestrated the construction of 300 arenas across Russia, and aim to build 300 more in the next half-decade.
“You know how many rinks we had in Soviet times?” Mr. Fetisov asks me on the bench, where players drink tea between periods. “Thirty – and we kicked your ass!”
He jabs my shoulder, as the Prime Minister laughs inside his caged helmet. The great Canadian-Soviet hockey series of the 1970s are seared in their minds, moments that reassured them of their supremacy.
Mr. Putin hands his teacup to an aide, and returns to the ice to practise more turns before the next period begins. (He clearly prefers offence to defence, whether it's the fact that he takes every face-off when on the ice or hovers around centre when the play is in his own end, waiting for a stretch pass.)
“He's remarkable,” Mr. Fetisov says of his pupil. “Look at the determination.”
I was among a group of six newspaper editors invited to Russia this week to interview Mr. Putin – all of us from Group of Eight countries, the international club he seems to respect most. The public-relations motive was apparent. Russia will be widely criticized after Sunday's vote, especially by its rival, the United States. Mr. Putin wants to get ahead of the story.
We were bused to Mr. Putin's state-owned dacha in Novo Ogarevo, a wooded property set back from the main road and protected by a towering iron gate on one side and open field on the other. Armed guards are stationed along a forest drive that leads past a helipad to the conference house, a two-storey, neo-classical mansion where he entertained U.S. President Barack Obama.
Down a hill, there is a more modern house, with indoor pool and gym, where Mr. Putin lives and starts most days with a vigorous swim (preferred stroke: butterfly) and a judo workout. (It is believed to be one of 25 homes he has access to, including a palace on the Black Sea.)
To no one's surprise, Mr. Putin is late, by two hours. He is notoriously so, even keeping the Queen waiting once for nearly an hour. While waiting, we are plied with hors d'oeuvre served by an abundance of liveried staff.
We are free to ask him about anything, knowing our three-hour dinner was being taped for state TV and would be posted on the Internet.
There are questions about corruption, his own staggering wealth, the troubled state of democracy in Russia and his marriage (his wife is rarely seen in public). He also expounds on the state of affairs in Syria, the European debt crisis and Arctic sovereignty, as well as his cool relationship with the Obama administration.
“Ask any question,” Mr. Putin declares. “I will answer anything.”