* Law allows Russian regions to let Putin choose leaders
* Direct elections of governors reintroduced only last year
* Critics say law reverses concession to opposition protests
By Alissa de Carbonnel
MOSCOW, April 2 (Reuters) - President Vladimir Putin signed a law on Tuesday letting him pick candidates to lead Russia's regions if local lawmakers scrap popular polls, in what critics called a setback for democracy in the Russian leader's new term.
The law allows each of the country's 83 regions to repeal direct elections of governors, introduced just last year in a concession during a wave of protests by Russians fed up with Putin's dominance and demanding a stronger political voice.
Putin has said the law is needed to protect the rights of minorities in ethnically mixed regions such as the mostly Muslim provinces of the insurgency-plagued North Caucasus.
The Kremlin is concerned that direct elections in the volatile regions could spark unrest or involve candidates whose loyalty is in question. Russia is holding the Winter Olympics next February in Sochi, close to the North Caucasus provinces.
But critics of the president say the law is a rollback in democracy that favours the ruling United Russia party, which is far less popular than Putin himself and had its parliamentary majority sharply reduced in a December 2011 election.
They fear the Kremlin and United Russia will use the measure to sideline opposition candidates in favour of loyal governors.
"It's another lever to manage everything from Moscow," said Boris Nemtsov, a prominent opposition leader and a former cabinet minister in the 1990s under Putin's predecessor, Boris Yeltsin.
Under the new rules, each regional legislature can vote to abandon direct elections, instead choosing their governor from a list of three candidates handed down by Putin.
Putin, in power as president or prime minister since 2000, scrapped popular elections of regional governors in 2004 as part of a drive to tighten his grip on the political system.
They were reintroduced last year amid the biggest opposition protests of his rule.
"It was a feint," Nemtsov said of their reintroduction. "Now Putin thinks the protest have faded and he has decided to roll back everything."
Putin has drawn criticism from Western governments and activists in Russia for what opponents say are restrictive laws, a crackdown on non-governmental groups and the prosecution of dissenters since he began a new presidential term in May. (Reporting By Alissa de Carbonnel; Editing by Alistair Lyon)