* Russian state TV runs constant footage of protest violence
* Kremlin wary protests may be spill over into Russia
* Putin woos Ukraine with bailout, plans Eurasian Union
By Timothy Heritage
MOSCOW, Feb 19 (Reuters) - A Ukrainian protester lobs a burning petrol bomb into a doorway, a police officer writhes in agony on the ground, smoke and flames rise from burning barricades.
Footage of violence in the Ukrainian capital was beamed almost non-stop into Russian homes by state television on Wednesday, accompanied by apocalyptic warnings of civil war next door and accusations of meddling by foreign states.
The pictures tell the story better than any politicians' words, ramming home the message that President Vladimir Putin wants to put across - the violence has got out of hand and must be stopped.
"Ukraine stands on a very dangerous threshold," said Mikhail Margelov, chairman of the foreign affairs committee in the upper house of Russia's parliament. "It's all following the regulation course for a country heading towards civil war."
Getting the message across is vital to build Russian public support for Putin's strategy in Ukraine, the second biggest of the former Soviet states and a country of 46 million that is at the heart of a geopolitical tussle between East and West.
His foreign ministry underscored Moscow's attachment to a Slavic, Orthodox Christian neighbour that was the cradle of Russian nationhood over a millennium ago by calling Ukraine a "friendly brother state" and strategic partner on Wednesday.
Putin has largely let others - and Russian money - do the talking for him during the crisis, saying almost nothing in public about at least four meetings has had with Ukrainian President Viktor Yanukovich over the past six months.
But his overriding goal in the dispute over Ukraine's now frozen deals to build trade and political ties with the EU has been clear - to keep Ukraine, a big market and a country many Russians see as an extension of their own, in Moscow's orbit.
That in turn fits with Putin's broader geopolitical aim of restoring power and global influence that was lost with the collapse of Soviet communism in 1991 - the tussle over Kiev is not only with the hesitant regional ambitions of the EU but with Moscow's old superpower adversary the United States.
Letting Ukraine turn to the EU, notably towards Russia's historic rival Poland, would send a signal inspiring other former Soviet republics to follow suit, including Georgia and Moldova, which are also negotiating trade pacts with the bloc.
And it might even encourage rebellion in Russia, offering hope to the mainly middle-class young urbanites who joined protests against Putin in the winter of 2011-12 but failed to end his 14-year domination of Russian politics.
At the same time, the violence plays, to an extent, into Putin's hands by enabling Russian media and officials to portray Yanukovich's opponents as a violent rabble backed by the West and bent on destruction.
The presence on the barricades of hard-right militants, some of whom honour anti-Russian, anti-Semitic groups that fought with Nazis against the Red Army, allows critics to label the opposition as "fascists" pursuing "pogroms" in Ukraine.
Such messages appear to be getting through, with Russians showing little support for the Ukrainian opposition.
As violence flared on Tuesday, a Moscow radio call-in discussed whether Yanukovich should use force against the protesters. One caller after another said he was right to resort to take action. One said the Ukrainian leader had shown weakness by failing to turn machineguns on the crowd.
Protests began in Kiev after Yanukovich ordered a policy U-turn in November, spurning a trade pact with the EU and rebuilding economic ties with Moscow instead.
The reward was a Russian bailout package offering cash-strapped Ukraine $15 billion and reduced gas prices.
A second, $2-billion tranche of the bailout loan may be tied to Yanukovich ending the unrest and refusing protesters' demands to bring opposition leaders into government.
Putin appeared to win those promises at talks with Yanukovich earlier this month during the Winter Olympics in the Russian Black Sea resort of Sochi.
"I think that Russia received some kind of assurances from the Kiev leadership which satisfied them," said Gleb Pavlovsky, a former Kremlin spin doctor who has worked in Kiev.
Russia, he believed, received assurances Yanukovich would "hold firm to his position in talks, not make big concessions, fight against the radicals who have got stronger in the opposition".
"Something along those lines and probably more concrete," Pavlovsky said. "I doubt that just words would reassure Putin."
Another incentive for Putin to keep Ukraine under Russia's influence is its importance to his project for a trade and political bloc stretching from China's frontiers to the edge of the EU.
Ex-Soviet Kazakhstan and Belarus have already joined a Moscow-led customs union which is a precursor of the Eurasian Union that Putin plans. But Ukraine is a much bigger market. Without it, the union would be much weaker.
Putin's spokesman reiterated on Wednesday that Russia would not intervene in Ukraine but Western nations accuse Moscow of meddling behind the scenes anyway. Russian media have hit back with similar accusations against Western politicians, including some who have visited the protesters in central Kiev.
One Kremlin aide, Sergei Glazyev, has floated the idea that Ukraine could become a federation giving more power to its regions - a move, he said, that might enable mainly Russian-speaking eastern Ukraine to join Putin's trading bloc.
That call has been taken up by parliamentarians in Moscow, fuelling speculation that this - or some form of annexation of Russia-speaking areas - may have the Kremlin's backing.
A former Putin adviser, Andrei Illarionov, has quoted unidentified Kremlin sources as saying a "solution" to the Ukrainian question must be found.
The options, he says, could include the "federalisation" of Ukraine to establish control over eastern and southern regions or otherwise trying to control Ukrainian cities with large Russian-speaking populations.
Western observers are also worried by calls in Crimea for the region to again become Russian territory, nearly six decades after Kremlin leader Nikita Khrushchev redrew internal Soviet boundaries in order to gift the peninsula to Ukraine.
Although Moscow has not responded to those calls, Russia would have reasons to embrace Crimea - Moscow's Black Sea fleet is based in the Crimean port of Sevastopol.
Civil war or a coup in Ukraine might also threaten other Russian industrial interests in eastern Ukraine, such as factories which have contracts with the Russian military.
"We have close brotherly ties, unified aviation, space and machine-building industries ... some industries are threatened with collapse," said Russian Communist leader Gennady Zyuganov.
Evoking memories of World War Two, when Ukraine was overrun by Nazi Germany and drawing comparison with the collapse of the Soviet Union in 1991, he said: "We must do everything to support the patriotic forces." (Editing by Alastair Macdonald)