By Karolin Schaps and Maria Golovnina

LONDON, Aug 17 (Reuters) - Dozens of people wearing balaclavas rallied outside the Russian embassy in London on Friday in support of the Russian feminist punk band Pussy Riot, just a day after activists hurled rocks at the building protesting Moscow's position on Syria.

The Russian embassy, in an upmarket part of central London, has seen many protests outside its iron gates in recent months by activists angry at Moscow's stance on a number of diplomatic issues as well as a political crackdown inside the country.

Wearing face masks, the crowd of about 40 people chanted "I say Pussy, you say Riot" outside the embassy just as three women from Pussy Riot were sentenced to two years in jail for their protest against President Vladimir Putin in a church.

"Russia is turning into a backward society," said Lisa Gornik, one of the protesters.

"I used to really love Russia, I studied Russian literature. It was all about freedom of Russia, beautiful sentiments of (Russian novelists) Tolstoy, Dostoyevsky. They must be turning in their graves now, thinking what has Russia become."

Hours earlier, protesters chanting slogans against Syrian President Bashar al-Assad, who enjoys Russia's support in his standoff with rebel forces and the West, attacked the embassy overnight, throwing stones and smashing windows.

"The police who arrived at the scene regretfully did not take any measures to stop the unsanctioned protest and detain the attackers," said an embassy spokesman. No one was hurt.

"This is not the first case of vandalism against the Russian Embassy in London this year," it said separately in a statement. "We view the incident as a new case of violation of the principle of inviolability of diplomatic missions in London.

The embassy said the attack caused significant damage to the building and posted pictures of broken windows and large rocks scattered on the floor on its Facebook social media page.

Moscow's support for Syria's government has been criticised by protest groups since the uprising began in March 2011. Russia and China have vetoed three Western-backed resolutions criticising Damascus and threatening sanctions.

Police said an investigation was underway but noted people in London were free to rally to express their views.

"The UK has a strong democratic tradition of allowing people to express their views and protest," police said in a statement.

"As one of the most diverse capitals in the world, with embassies and organisations from across the world represented here, protests and demonstrations take place in London every day."

Britain's relations with Russia have been sour since the 2006 murder in London of Kremlin critic Alexander Litvinenko, a former Russian spy who died from poisoning by radioactive polonium-210. (Additional reporting by Michael Holden; Writing by Maria Golovnina; Editing by Jon Hemming)