(Repeats story first published on April 13, text unchanged)
* Putin's popularity soars over taking back Crimea
* Risks losing influence in Ukraine, which votes on May 25
* Russian elites back Putin, but show signs of unease
By Timothy Heritage
MOSCOW, April 13 (Reuters) - Vladimir Putin looks likely to go down in history as the Russian leader who won back Crimea, but he is fighting to avoid also being remembered as the man who let Ukraine escape from Moscow's sphere of influence.
The next six weeks will be decisive in that battle as Ukraine prepares to elect a president on May 25, agree a new constitution and prevent pro-Russian separatists in the east breaking away.
Reclaiming Crimea 60 years after it was gifted to Ukraine by Soviet leader Nikita Khrushchev, apparently on a whim, has been a domestic triumph for Putin. But losing the ability to exert influence over Ukraine would be a high price to pay for that and might, with time, seriously detract from the achievement.
Even though Ukraine and Russia ceased to be in the same country when the Soviet Union fell apart in 1991, economic, political and cultural links remained strong and Moscow retained a lot of political and economic influence in Kiev.
"Putin is now looking for a model where Moscow retains some degree of influence," said Gleb Pavlovsky, a former Kremlin spin doctor.
"I think the next six weeks will be key because Putin can't afford to let the Ukrainian election produce an unacceptable formula for Russia and he can't afford to look indecisive.
"He needs a quick solution."
Yet at first glance, Putin does not look to have an urgent problem. His ratings have risen to their highest in years since Russian forces took over Crimea and Moscow annexed the peninsula after a hastily arranged referendum among its 2 million people.
Moscow's political and business elites rallied behind Putin as the West imposed sanctions over what its leaders called an illegal redrawing of borders that revived Cold War-era conflict.
He signed Crimea's annexation last month after setting out dreams of a greater Russia in a speech greeted by cheers in the Kremlin. His vision of repairing the break-up of the Soviet Union would bring the "near abroad" back under Moscow's wing.
The show of unity behind the Russian president is likely to continue for a some time, and the political opposition in Moscow has for now been neutralised by Putin's success in Crimea.
SIGNS OF UNEASE
But business and political sources say there is growing unease beneath the surface as the euphoria fades and the harsh reality sets in of Western sanctions - and the prospect of more if Russia does not cooperate with the West.
With Russia's economic growth stuttering almost to a halt, and capital flight rising to nearly $64 billion in the first three months of this year, there is plenty of cause for concern about taking on the financial burden of propping up Crimea - a region long on pensioners and faded Black Sea resorts.
Some business leaders and government officials are also worried by the war of words with the West, a threat of a return to Soviet-era isolation after two decades of building relations with richer states and even hostility abroad towards wealthy Russians and their children studying at foreign institutions.
"There are people who are disorientated. They won't say this in public but there is a split over whether what is happening is good for the country," said a Russian businessman in Moscow with liberal political views who did not want to be identified.
Political scientist Stanislav Belkovsky went further in an interview with liberal radio station Ekho Moskvy, suggesting the mood had started to change since U.S. sanctions hit members of Putin's inner circle as well as other individuals and officials.
"Two weeks ago the Russian elite were in a state of euphoria," he said. "It seemed Russia had won a huge geopolitical victory and we should be proud.
"Now, today, the elite are slipping into in a state of mild depression. They understand that a problem is coming.
"So when real sanctions hit, when people realised the real estate, healthcare, education in the West, which they have got used to in the last 20 years were in danger, they got worried."
Although such concerns are likely to remain below the surface in a political climate where criticising Putin over Crimea has become all but impossible, his ability to retain Moscow's influence in Ukraine will be crucial to his capacity to maintain popular support for his actions.
Moscow's influence in Kiev has been under threat since President Viktor Yanukovich fled to Russia on Feb. 22 after three months of protests sparked by his decision to spurn political and trade agreements with the EU and strengthen economic ties with Moscow instead.
The installation of a government that looks West instead of East has increased the danger for Russia of losing its ability to steer events in a country it regards as a buffer between it and the West and as the historic cradle of Russian civilisation.
For many of Russia's 144 million people, bonds to Ukraine's 46 million are familial and emotional, though for the Kremlin and its allies in business, Ukraine's industries, concentrated in the Russian-speaking east, and its markets, are also a draw.
For supporters of the new Ukrainian government's pro-Western course, Putin is also concerned not to let Ukraine flourish in a way that might inspire his Russian opponents to try to emulate the "Euromaidan" protesters of Kiev and overthrow the president.
Central to Putin's tactics now is a build-up of troops on the border with Ukraine, a show of force that has fuelled fears in Ukraine and the West that he could send in troops to annex eastern regions such as Donetsk, Luhansk and Kharkiv where Kiev accuses Moscow of fomenting unrest and backing separatists.
The Ukrainian government said on Sunday it was sending security forces into the eastern city of Slaviansk where the pro-Russian militants have seized control of the local police headquarters.
Putin has his loyal parliament's consent to use the army if Russian speakers are deemed to be in danger - a tactic familiar from Crimea. Russian state media have paved the way for this by depicting Ukraine as beset by marauding groups of neo-fascists.
But sending in the troops would risk a new, much tougher round of Western sanctions or even a military conflict which could be costly, inflict heavy Russian losses and dent the 61-year-old president's popularity.
The border build-up may be mainly a negotiating tactic with Western leaders: "The military are there in principle so that people agree to talk to Putin about Ukraine's future," said Pavlovsky, who advised the president until three years ago.
"Putin realises that if there is no risk of the crisis worsening, no one will bring him into discussions on Ukraine."
BIG BROTHER IS WATCHING
The troops also serve as a reminder to Ukraine's new leaders that "Big Brother" is watching and is still a force to be heeded. They provide the backdrop as Russia pushes its demands, in daily Foreign Ministry statements lambasting the West and Ukraine's government, and in public remarks led by Putin and by his wily and experienced foreign minister, Sergei Lavrov.
Threats to cut off gas supplies to Ukraine over its $2.2 billion unpaid bill, raising the prospect of disruptions to deliveries to western Europe that pass through Ukraine, also keep pressure on Kiev and help Russia to press its demands.
The Russian demands, sure to be outlined at talks in Geneva on Thursday with the United States, EU and Ukraine, include an insistence that Ukraine remain outside NATO and the EU, that its regions are given more autonomy and Russian speakers guaranteed more rights to use their language rather than Ukrainian.
The idea of a federal system of governance for Ukraine has been floated for several months by the Kremlin. In February, Putin's lead adviser on Ukraine suggested regions might even pursue different foreign policies, the industrial east aligning with Russia and the Ukrainian-speaking west embracing the EU.
Viewing that as a mandate for more Crimean-style referendums on secession, Kiev has promised to devolve powers to the regions but rejects "federalism". It has also shown sensitivity to Russian speakers' rights by dropping plans for a law enforcing the use of Ukrainian for official purposes.
Moscow made no secret of supporting Yanukovich and cannot expect to find his successor at all as sympathetic as the former governor of Donetsk - but Ukrainian leaders are all well aware that feuding with Russia can only hurt them in the long run.
Even if Moscow cannot hope for a president who openly favours Russia, it can see to it that any future leader will be obliged to seek a working balance in relations between east and west. If Putin has his way, he will be able to show Russians he has done all he can to keep Moscow's influence in the country.
Kremlin aides insist Putin is not concerned about his place in history and is driven by the best interests of Russia. The verdict on his action may, in any case, be a long time coming.
Arguing that losing influence in Kiev was not inevitable after snatching Crimea away from it, Boris Makarenko of the Centre for Political Technologies in Moscow said: "The two are not mutually exclusive.
"I only know that history is wiser than any of us - and its verdict is never delivered in haste." (Editing by Alastair Macdonald)