A Russian court on Thursday slapped a series of small fines on Google for failing to take down contentious YouTube videos about the Kremlin's military operation in Ukraine.

The Moscow court ordered the US tech behemoth to pay a total of 11 million rubles ($135,000) for ignoring the state media regulator's orders to remove posts alleging heavy Russian losses in Ukraine.

One of the videos showed an alleged phone conversation between Russian soldiers and their relatives back home in which the troops complained of numerous casualties in their ranks, Russian state news agencies reported.

Another alleged that soldiers who were trying to move back from Ukrainian counter-offensives were being shot by retreat-blocking Russian detachments, the state media reports said.

Google's ubiquitous video hosting service has been in Russia's crosshairs throughout its nearly two-month campaign in Ukraine.

The tech giant infuriated Russian officials by blocking the lower house of parliament's official media channel earlier this month.

Russia has moved swiftly to cut access to non-state media and information resources since the launch of its operation in February 24.

Russian courts have banned Facebook and Instagram, calling them "extremist" organisations, as well as Twitter.

All three are still accessible through VPN services, which try to disguise user locations.

But most Russians get their news from state television and other government-controlled media outlets, which follow strict rules on covering the military campaign.