* Putin outlines infrastructure investment plan
* Russia's Rosneft to double oil flows to China
* Investors gloomy over Russia's economy
ST PETERSBURG, Russia, June 21 (Reuters) - President Vladimir Putin unveiled a $13 billion investment plan on Friday to build new roads and railways by tapping a reserve fund, hoping to revive Russia's economy and avoid stagnation.
But in a speech setting out moves to curb inflation, boost economic growth and tighten control of under-performing state firms, he failed to allay investors' concerns over an economy that is sliding towards recession.
With growth slowing and inflation high, even the promise of a lucrative energy deal with China valued at $270 billion could not lift the gloom at Russia's answer to Davos.
Putin was less upbeat than in previous years at the annual business forum in his hometown of St Petersburg, an event meant to show Russia is a good place to invest, and acknowledged the economy faced problems a year into his third spell as president.
"There is no magic wand which could change the situation with one wave," he said, declaring the era of high revenues from oil exports over.
He said he would plough 450 billion roubles ($13.6 billion) into constructing a new ring road outside Moscow, updating the Trans-Siberian railway to Russia's Far East and building a high-speed rail link from the capital to Kazan in central Russia.
He said he would do so by drawing on funds from the $87-billion National Welfare Fund, a rainy-day stash of windfall oil revenues intended to provide for pensions.
"This money must work for Russia's economy, for the country's future," Putin said, outlining plans that underline Russia's growing interest in Asia as it develops its economy.
Moves to improve infrastructure, some of which has improved little since Soviet times, are considered vital by investors to modernise Russia and make its economy more competitive.
But with inflation running at an annual rate of 7.4 percent, growth now forecast to be 2.4 percent this year, below Putin's 5 percent target, he did not go far enough for some economists.
"I support the approach of paying closer attention to our infrastructure, but of course we need to spend much more than was announced," said former Finance Minister Alexei Kudrin.
Kudrin voiced concern that Russia might fritter away money that could be vital to stave off any future financial crisis. He was in office when Russia tapped its reserves to help see it through the 2008-09 economic meltdown.
FEARS OF STAGNATION
Some investors are worried that, despite his promises, Putin cannot carry out the reforms needed to lift the economy such as reducing its heavy reliance on oil exports.
"There is a concern that Russia is potentially in some Brezhnev-style stagnation," said Charles Robertson, chief economist at investment bank Renaissance Capital, referring to the Soviet leader Leonid Brezhnev.
"Now the energy prices are stagnating as they did in the late 1970s and the early 1980s, and now maybe reforms are petering out. Maybe politics is a part of the problem," he added.
Last year Putin, 60, faced the biggest protests since he was first elected president in 2000. The rallies have dwindled but critics accuse Putin of cracking down hard on opponents to silence dissent and stifle democracy.
Putin told an audience including foreign investors, Russian business leaders and German Chancellor Angela Merkel that Russia would curb inflation by tying the tariffs charged by state monopolies such as energy firms to retail price growth.
He praised the deal sealed by state-run Rosneft which will double Russian oil flows to China and underlines Moscow's growing turn to Asia instead of Europe.
"The infrastructure projects are extremely important," German Gref head of state bank Sberbank, said. "In principle it's the right area (for development)."
But many investors are worried by the flight from Russia of a liberal economist, Sergei Guriev, after pressure from state prosecutors, and by signs that turf wars between political and business elites are intensifying.
"There's a pretty remarkable consensus for what's wrong with the investment climate and it starts with rule of man as opposed to rule of law," said Bernie Sucher, of Aton investment group.
Putin's day was also marred by a dipomatic spat when, visiting an art exhibition together, Merkel told him German art seized by Soviet forces after World War Two should be returned to Germany. He rejected this.