* Putin to run for president in 2012
* Medvedev set to be prime minister
* Some economists fear stagnation under Putin
By Thomas Grove and Gleb Bryanski
MOSCOW, Sept 25 Russian Prime Minister Vladimir Putin has ended months of speculation by saying he will run for president next March in an election that could open the way for him to stay in power for 12 more years.
Putin's announcement was greeted by a standing ovation on Saturday at a congress of his ruling United Russia party, but it alarmed critics who say his return to the presidency could herald an era of political and economic stagnation.
He and President Dmitry Medvedev have ruled in a power 'tandem' since Putin was forced by the constitution to yield the presidency in 2008 after serving a maximum two consecutive terms.
Putin, 58, accepted a proposal by Medvedev to return as president in the carefully choreographed congress in a Moscow sports stadium.
"I want to say directly: (Medvedev and I) reached an agreement between ourselves long ago, several years ago, on what to do in the future, on who should do what," Putin said.
"But both I and Dmitry Anatolyevich Medvedev believe that this is far from being the most important thing -- who will do what, who will sit in what place. What is far more important is something else: how we will all work, what results we achieve, and what the citizens of our country think of this."
Over 11 years in power, Putin has cultivated the image of a vigorous leader and been filmed riding bare-chested on horseback, scuba diving and showing off his judo skills.
His policies -- crushing a Chechen separatist rebellion, taming super-rich businessmen and bringing wayward regions to heel -- have similarly won him popularity among Russians.
Putin, described in leaked U.S. diplomatic cables as the "Alpha dog" in the tandem, proposed his younger and more liberal protege replace him as prime minister after the election to lead a young reformist government.
FEARS OF STAGNATION
But critics say his return to the Kremlin, virtually unopposed, could bring back memories of the economic and political stagnation under Soviet leader Leonid Brezhnev in the 1970s and early 1980s.
"It's a sign of growing stagnation in the Russian political elite and it means that Mr Putin, if elected, can rule for another 12 years until 2024," said Yevgeny Volk, deputy director of the Yeltsin Foundation.
The next president will be elected for six years and the constitution still allows the head of state a maximum of two straight terms -- meaning Putin could be in power for another 12 years.
Washington said it expected to keep making progress in the "reset" in relations with Moscow, whoever was the next Russian president.
"While we have had a very strong working relationship with President Medvedev, it's worth noting that Vladimir Putin was prime minister throughout the reset," White House spokesman Tommy Vietor said.
Putin proposed Medvedev, 46, to lead United Russia's list of candidates for a parliamentary election on Dec. 4.
The move is intended to help reverse a decline in support for United Russia and boost its hopes of retaining a two-thirds majority in the State Duma lower house.
Investors had been urging that Putin and Medvedev put an end to the political uncertainty that has deterred many from putting money into the $1.5 trillion economy of the world's largest energy producer.
"Market turmoil has hit Russia hard," said Charles Robertson, head of macro-strategy at emerging markets investment bank Renaissance Capital.
"With less political uncertainty, the authorities may hope that capital flight eases, and that some may return capital in coming months to take advantage of cheaper asset prices."
As president from 2000 to 2008, Putin oversaw an economic boom where household incomes improved on the back of a rise in global oil prices, and his tough talking and macho image helped restore Russia's self-confidence on the world stage.
But Putin, who was once a KGB officer in East Germany, is widely seen as more conservative than Medvedev and critics accuse him of riding roughshod over human rights and democracy, and expanding the power of the security forces.
Some economists say his return to the Kremlin makes it less likely that Russia will carry out much-needed changes such as pension reforms and reducing Russia's dependency on natural resources. Oil and gas revenues make up half the budget.
Others say Putin and Medvedev differ more in style than policy. (Reporting by Timothy Heritage, Guy Faulconbridge, Gleb Bryanski, Steve Gutterman, Alexei Anishchuk, Douglas Busvine and Thomas Grove; editing by Ralph Boulton and Kevin Liffey)