Russia's main opposition leader Alexei Navalny on Thursday blamed mass police raids on his regional offices on Kremlin "hysteria" sparked by the ruling party's losses in local elections.

"Why such hysteria? Two words: 'Smart voting,'" Navalny said on his blog.

Navalny said police searches were underway at more than 200 addresses in 41 cities across Russia.

He called it "the largest police operation in modern Russian history" and said it was the result of his call to supporters to vote tactically to push out ruling party candidates in local elections held Sunday in Moscow and other cities.

Allies of President Vladimir Putin suffered major losses in Moscow as a result.

"Putin got upset and is stomping his feet," the 43-year-old opposition leader said.

Navalny said authorities wanted to "demoralise" Russians and force them "to renounce collective action".

He said on Twitter that investigators' vans had arrived outside his Moscow headquarters as well.

Russian investigators in August launched a money laundering probe against Navalny's Anti-Corruption Fund (FBK), which has worked to expose officials' questionable wealth.

In the run-up to the elections Navalny and his supporters organised a wave of protests after popular opposition politicians were barred from standing in the Moscow parliament election, prompting a police crackdown.