* Sochi 2014 flame embarking on 65,000 km torch relay around Russia
* In patriotic ceremony, Putin says dream is coming true
* Flame to travel to North Pole, mountain peak, outer space
* Sochi Winter Games take place in February (Adds flame briefly goes out, final paragraph)
By Denis Dyomkin and Steve Gutterman
MOSCOW, Oct 6 (Reuters) - President Vladimir Putin hoisted the flame that will burn at the Sochi 2014 Winter Games high in Red Square on Sunday, bringing his personal campaign to stage Russia's first post-Soviet Olympics within sight of completion.
Declaring that "our shared dream is becoming reality," Putin signalled the start of a 123-day, 65,000 km (40,000 mile) torch relay that will take the flame to the North Pole and outer space before the Olympics begin in the Black Sea resort on Feb. 7.
The relay "will show the world Russia the way it is and the way we love it," Putin told the crowd in an elaborate ceremony, calling it a country of diverse people "united by common aims and by pride in their great homeland."
As expected, Putin made no mention of controversies clouding the Games, such as a law critics say discriminates against gays and concerns about a ban on most rallies in Sochi, or of the Islamist insurgency that persists not far away.
Protected by four small lanterns, the flame was flown in from Greece after being lit at the birthplace of the ancient Olympics and handed over to Russia on Saturday at the marble Athens stadium that hosted the first modern Games in 1896.
But from the jet's arrival to Putin's patriotic speech, the accent was on Russia and its president, who has staked his reputation on a safe, successful Sochi Olympics - the first Winter Games it has held.
As images of rockets and ballerinas flashed across a giant screen on Red Square, rap rhymes from dancers in white, red and blue of Russia's flag alternated with chants of "Russia! Russia!"
With the colourful onion domes of St Basil's Cathedral behind him, Putin strode across the cobbles on a red carpet as a medley that included part of imperial-era anthem "God Save the Tsar" played.
"Today is a joyous and momentous day," Putin said. "The Olympic flame - the symbol of the planet's main sports event, the symbol of peace and friendship - has arrived in Russia, and in a few minutes it will be on its way around our huge country."
The choreographed celebration did not all go according to script, however.
There was a nationally televised moment of embarrassment early in the torch relay, when the flame went out as a portly former swim champion carried it through a Kremlin gate.
He looked around for help and a guard standing by the pathway came to the rescue with a cigarette lighter.
The flame had been brought to Moscow by Deputy Prime Minister Dmitry Kozak, who stepped off the jet as a military band played and an honour guard of rifle-toting soldiers in woolly Astrakhan collars stood by, chins jutting high.
"We - all Russians - have a right to be proud," Kozak said.
Escorted part way by leather-jacketed bikers from a motorcycle club whose leader is a friend of Putin's, a convoy bore the flame into central Moscow and it was carried onto Red Square on a clear, crisp autumn afternoon.
Like the plane that brought the flame from Athens, the square outside the Kremlin was decorated with a Firebird-inspired design drawing on Russian folk patterns, echoed on the jackets of smiling, waving young men and women who walked behind Putin.
The dark stone mausoleum where the embalmed body of Bolshevik Revolution leader Vladimir Lenin still lies was hidden behind a stage and a mock-up of snow-white peaks representing the mountains above Sochi where alpine events will be held.
The longest torch relay before a Winter Olympics seems designed to celebrate a spirit of exploration and conquest as well as Russia's variety and most of all its sheer scale, taking the flame though all 83 regions spanning 10 time zones.
It will go to the North Pole on an atomic-powered icebreaker, to Europe's highest peak, Mt Elbrus, to the depths of Siberia's Lake Baikal and to the International Space Station, whose crew will take the torch - unlit - on a spacewalk.
More than 90 percent of Russia's people will be within an hour of the flame - a way to encourage them to feel involved.
But six years after he secured the 2014 Games for Sochi with an impassioned pitch, it is Putin - who turns 61 on Monday - who is the most invested in making the only Olympics staged in an independent Russia a success.
Putin has faced international criticism over a law he signed this year prohibiting the spread of gay "propaganda" among minors, which activists and Western governments say is discriminatory and curtails basic human freedoms.
Critics have also questioned the $50 billion cost and the wisdom of holding the Winter Games in a subtropical locale, and have called a security decree Putin signed draconian because it restricts movement and bans rallies unrelated to the Olympics. (Writing by Steve Gutterman, editing by Justin Palmer and Martyn Herman)