* Simultaneous raids in at least 41 towns and cities
* Searches are part of money-laundering investigation
* Navalny's allies say investigation is trumped up
* Election monitor says its activists also targeted (Updates with Navalny quotes, number of raids)
By Andrew Osborn
MOSCOW, Sept 12 (Reuters) - Russian law enforcement authorities on Thursday carried out mass raids on the homes and offices of Kremlin critic Alexei Navalny's supporters across the country, a move he described as the biggest crackdown of its kind in modern Russian history.
More than 200 searches took place as part of an investigation into money-laundering in 41 towns and cities, Navalny said. CCTV footage showed masked men using power tools to remove doors and armed officers securing various premises associated with Navalny's political movement.
The raids happened four days after the ruling United Russia party, which supports President Vladimir Putin, lost a third of its seats in the Moscow city assembly while easily retaining its dominant nationwide position.
Navalny, whose own allies had been barred from running in the Moscow city election, had urged people to vote tactically to try to reduce the chances of Kremlin-backed candidates, a strategy that appears to have had some success in the capital.
"Putin is very angry and is stamping his feet," Navalny said in a video released on Thursday. "I congratulate you. Today the biggest police operation is modern Russian history is taking place."
Authorities told activists that the searches were related to a money-laundering investigation into Navalny's Anti-Corruption Foundation, an organisation that has published embarrassing investigations into what it says is the wrongdoing of corrupt officials.
State investigators last month opened a criminal investigation into the alleged laundering of 1 billion roubles ($15 million) by the foundation itself. It also froze a number of bank accounts linked to the foundation, a move Navalny's allies said was a trumped-up attempt to cripple his political movement.
Kira Yarmysh, Navalny's spokeswoman, said the scale and nature of the latest raids was unprecedented.
Leonid Volkov, another senior Navalny ally, published a list of towns and cities where activists had been targeted.
He linked the searches to Navalny's tactical voting strategy and said the homes of activists, their relatives and the regional headquarters of Navalny's movement were being targeted.
Activists were being taken in for questioning, he added, saying technical hardware was being confiscated.
"The state has two tasks - to frighten and steal," wrote Volkov. "It's obvious that the aim of this operation is to destroy our headquarters structure and to obstruct the work of our (regional) headquarters."
Navalny, a 43-year-old lawyer and activist, was jailed in July for 30 days after calling for people to demonstrate over the exclusion of opposition candidates from the Moscow election.
The authorities' refusal to register opposition candidates, including some of Navalny's allies, on technical grounds triggered the biggest sustained protest movement in Russia since 2011-2013 with up to 60,000 people demonstrating at one point.
Police briefly detained more than 2,000 people this summer, handed short jail terms to almost Navalny's entire entourage and used force to disperse what they said were illegal protests.
Golos, a non-governmental organisation that monitors Russian elections, said on Thursday that the homes of its activists had also being raided by the authorities. ($1 = 65.1300 roubles) (Additional reporting by Maria Tsvetkova; Editing by Hugh Lawson and Giles Elgood)
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