On an overcast day in May, a clutch of the world's most powerful investors gathered in a 19th-century mansion in Moscow to hear a proposition from Vladimir Putin: invest in Russia, and we will invest with you.

For forty minutes at the government's Vozdvizhenka guest house, the prime minister addressed private equity and sovereign wealth funds representing a combined $2 trillion of wealth. He was pitching a plan to launch a $10 billion state-backed fund that Russia hopes can win over those foreign investors who still regard the country as a no-go zone.

There was a lot of back and forth and some tough questions, one participant said, as guests pressed Putin to convince them that the rewards of investing in Russia can outweigh the risks.

Can the Kremlin turn that image around? For many potential investors Russia is synonymous with corruption, weak rule of law and political risk, its reputation hurt by events such as the jailing of oil tycoon Mikhail Khodorkovsky. In a straw poll at a major private equity conference in Boston last week, Russia was ranked as the least attractive investment destination of the BRICs -- Brazil, Russia, India and China. Russians themselves are moving money out of the country to hedge their bets ahead of a presidential vote next March, and even President Dmitry Medvedev has called the investment climate very bad.

I could not agree more with the folks that decided not to vote on Russia (in the straw poll), said David Roux, co-founder of U.S. private equity fund Silver Lake, who was not at the meeting in Moscow. It is a high-potential place but ... it is easy to get your money in and almost impossible to get it out.

But Moscow says it has listened to the complaints and wants to use the new fund to change perceptions.

Many investors have not done any business in Russia, who only read the newspapers and the different horror stories, said Kirill Dmitriev, the new fund's first head.

PUTIN'S PITCH

The May 18 gathering was a radical departure for Putin, who normally receives foreign executives when they seek his personal blessing to close multi-billion-dollar deals.

Speaking through an interpreter to guests including Blackstone's Stephen Schwarzman and Abu Dhabi's Hareb Al Darmaki, he spelled out how the fund would work alongside foreign investors to buy businesses in Russia.

The response was encouraging. Lou Jiwei, head of sovereign wealth fund China Investment Corp., went on the record to say the fund could be a flexible way to attract foreign investment while Bader al-Saad, managing director of the Kuwait Investment Authority, said it would give us the opportunity to increase our direct investment in Russia.

Sovereign wealth funds managing hundreds of billions of dollars are looking to diversify their risks, particularly away from the bulging debt of developed nations that might be tempted to inflate, or even default, their way out of trouble.

Experts say the fund, with its inbuilt political insurance, is designed to meet their needs. It's a very innovative and creative way to tap into long-term investors, said Ashby Monk, co-director of Oxford University's analytical Sovereign Wealth Fund Project. If I were looking for a partner for private equity investments in Russia, the Kremlin would be top of my list.

ROLLOUT

The Russian Direct Investment Fund (RDIF) will be launched at the St Petersburg International Economic Forum -- Russia's answer to Davos -- this week. The product of over a year of soundings with foreign investors, the fund will receive $2 billion in state cash each year for five years.

Its structure mimics the private equity model: it would make direct investments of $50-$500 million in firms geared to the growth of Russia's middle class, in sectors like healthcare, IT or infrastructure. Foreign investors would take the lead, and the fund would restrict itself to a minority role.

We came up with something that is very unique, and I think very positive, says Dmitriev, a 36-year-old Stanford and Harvard alumnus who made his name in Moscow with Delta Private Equity Partners, a Russia-focused fund that he co-ran.

The RDIF can only invest if foreign investors put up at least a matching sum. That will align its interests with its partners' and put a focus on returns which has been lacking in previous initiatives such as special economic zones and Rusnano, a state nanotechnology investment vehicle.

If we can show to foreign investors that they can consistently make a reasonable return in Russia, they will put in a dollar now, and in three or four years they will put in $10, Dmitriev told Reuters.

He reckons the RDIF could attract as much as $50 billion in co-investment over the next 5-7 years. That capital is sorely needed in Russia, where investment is only around 20 percent of GDP -- less than half China's level.

GETTING ALIGNED

Russia's dependence on oil and gas, which account for two-thirds of exports and over half of federal budget revenues, was not a problem during the past decade when rising oil prices drove annual growth rates of 7-8 percent.

But the crash of 2008 sparked an economic contraction of 8 percent the following year, and exposed weaknesses including Russia's over-reliance on foreign credit, a depleted capital stock and low productivity.

Russia has made progress in reducing its vulnerability to external shocks by strengthening the banking system. Hedge fund manager Viatcheslav Pivovarov said the fund marks a further step toward creating a broader base for growth.

Pivovarov, who returned from stints at New York hedge funds Third Point and Old Lane to advise the government on the fund, said it would help by meeting the common needs of the state and foreign investors. The fund aligns the interests between foreign investors -- strategic or portfolio -- and the Russian participants because the government is putting its money where its mouth is, said Pivovarov, now managing partner at Altera Capital, a $350 million Russia-dedicated startup fund.

$2 TRILLION IN THE ROOM

Given Russia's record, the project was bound to meet skepticism. But the investors at Vozdvizhenka, renamed in the Soviet era as the House of Friendship with the Peoples of Foreign Countries, came away liking what they heard during two days of briefings by top officials.

People in the room said they had the impression that both Putin and Medvedev, who floated the fund idea at the Davos World Economic Forum in January, strongly backed the project. That might reduce the risk of it being torpedoed by any tensions that could emerge between the two in the run-up to next year's presidential election.

It was very clear at the meeting that Putin is seriously committed to this venture, said a western investor, who declined to be named because of the sensitivity of the matter. It is a very hopeful sign that they have appointed as a CEO an individual who is a highly competent professional ... There was certainly no evidence at the meeting that this was going to be a 'friends and family' thing. That is encouraging.

A second western investor who has been skittish said he had heard enough to reconsider. They put a ton of thought into taking away the excuses why you wouldn't invest, said the investor, who also requested anonymity. I had a better view of investing in the country coming out of that meeting.

The RDIF would have a 5- to 7-year investment horizon and allow investors to sell out even if their partner wanted to stay in: a tweak included on the wishes of investors concerned that they may not be able to get their money out of Russia.

FOREIGN CASH IN, RUSSIAN CASH OUT

But while Moscow is hard at work selling the project, rich Russians are sending their money offshore. Net private sector capital outflows, which spiked in 2008, have been rising again since Medvedev ousted Moscow Mayor Yuri Luzhkov last year. The outflows exceeded $20 billion in the first quarter of 2011. Some of that, though not all, represents capital flight as oligarchs and officials seek safety abroad ahead of the presidential vote, when either Putin or Medvedev will run.

Then there's the question of whether the state can pick winners. Investors point to the remarkable success of the $1.4 billion U.S. float last month by Yandex -- known as the Russian Google. That deal, a pure private equity play, delivered a 500-fold payout to investors who bought into the internet startup in 2000.

One Moscow-based investor said the fund's relatively complex investment process meant it would be hard for it to pull off a repeat of the Yandex story, although it would reduce the risk of losing money. But he warned the Kremlin's involvement may reduce the returns, as well as the risks.

It's bets with capped upside. If they got lucky the state would be, like, that's too much money. So it's heads you win a bit and tails you don't lose.

(Douglas Busvine reported from Moscow, Megan Davies from New York, Dinesh Nair from Dubai; Editing by Simon Robinson and Sara Ledwith)