By Lidia Kelly and Douglas Busvine

MOSCOW (Reuters) - Russian Prime Minister Vladimir Putin sought on Thursday to win the support of small investors for his bid to return to the Kremlin by promising to make good losses on shares they bought in the 2007 stock market float of VTB bank.

Putin's pledge triggered a 3 percent rally in shares in the state-controlled bank, and overshadowed unusually frank discussions about state corruption at an investor forum held just over a month before Russia's presidential election.

The 59-year-old premier is front-runner to win the election but faces a groundswell of resentment among Russia's urban middle class that has spawned large street protests demanding fair elections and clean government.

"Citizens should know that we will do everything possible to ensure that they do not have any losses. We are ready to make available the necessary funds," Putin said in answer to a question from the floor at the Davos-style event in Moscow.

Eyeing VTB chief executive Andrei Kostin in the audience, Putin asked how much the buyback would cost.

Doing some rapid mental arithmetic, Kostin said compensating 100-110,000 investors would cost $500-$600 million. He promised to report back by Monday.

Turning to conference host German Gref, chief executive of state-controlled Sberbank, Putin said: "If you don't have enough money then you should borrow from Gref at Sberbank."

Gref, forcing a smile, answered: "We are a small, poor bank and we don't have that sort of money." Gref, who later said Putin had taken him completely by surprise, runs Russia's top bank with a market capitalization of $68 billion.

Shares in VTB have fallen by half since it raised $8 billion in an initial public offering in 2007. It appears likely that only small investors who took part in the "people's IPO" would be compensated, but not qualified, professional investors.

"It clearly was a joke. The state is going to buy back banks when they're trying to sell them?" said conference guest James Fenkner of Red Star Asset Management, adding large investors could not expect to be reimbursed. "The market completely got it wrong. I think it's a misconception, not serious at all."

Putin's spokesman, Dmitry Peskov, said no compensation was being considered for investors who have lost money on share sales by other state companies.

In another headline-grabbing move this week, Putin ordered VTB to bail out a tour operator that collapsed, stranding 1,400 tourists abroad in Thailand, Vietnam and the Dominican Republic.

Opposition politicians rounded on Putin for ordering the tourist rescue, saying it would come at the expense of VTB shareholders and the taxpayer.

TOUGH QUESTIONS

Putin's comments livened up a day of debate during which speakers - including his former finance minister, Alexei Kudrin - were unusually forthright in their criticism of state corruption and pressure on business in Russia.

Kudrin, who resigned last autumn in a row over ballooning defense spending, ruled out serving in Russia's next government and expressed sympathy with opposition protests against alleged ballot fraud in December's parliamentary election.

"The protests show that political competition and maturity are growing - that's something we need," he told an earlier panel discussion. "It's a positive sign of the times. We need to get used to the idea of opposing the powers that be."

Going further, liberal economist Sergei Guriev hit out at corruption, bloated state corporations and pressure by officials on business.

"The Russian state is not capable of solving problems - it is the problem itself," said Guriev, rector of Moscow's New Economic School.

Net capital outflows, which last year totaled $84 billion - or nearly 5 percent of gross domestic product - show that "investors believe that the Russian state has given up the fight against corruption," he added.

Kudrin joined a disparate group of opposition leaders on the stage at a large protest rally in Moscow on December 24, and a further demonstration is planned for this Saturday in Moscow to call for fair elections.

"It's a good thing to see - I'm glad to see the people on the streets, glad to see that people are not accepting the overhang of corruption and lack of openness," Nobel prize-winning U.S. economist Paul Krugman told Reuters at the event.

Krugman later shared the podium with Putin, who robustly defended his achievements during 12 years in power, first as a two-term president and then as prime minister.

"We have completed the post-Soviet stage of our development," Putin said, rattling off a string of statistics to back up his case - poverty rates halved, record-low inflation, a budget surplus, low public debts and rising life expectancy.

Putin also sought to turn the tables on his critics in the West, upbraiding governments for sliding into a debt trap, and teasing Krugman, who made the journey to Moscow despite coming down with a cold.

"Paul flew in - we'll make him well," he quipped.

(Additional reporting by Gleb Bryanski; Writing by Douglas Busvine; Editing by Sophie Hares)