Russia's communications watchdog on Monday gave Google 24 hours to delete what it called prohibited content or be fined and said Moscow could eventually slow down the company's traffic in the country.
Russia has already placed a punitive slowdown on US social network Twitter for not deleting banned content, part of a push by Moscow to rein in Western tech giants and beef up what it calls its internet "sovereignty".
The watchdog, Roskomnadzor, said it had sent more than 26,000 calls to Google to remove illegal information, including videos containing information on drugs or violence and material from what it called extremist organisations.
Google will be fined between $10,800-$54,000 if it does not restrict access to the banned information, Roskomnadzor said.
A repeat offence would be punishable by a fine of up to 10% of the company's total annual revenue, it said.
Google Russia did not respond to a request for comment about the watchdog's deadline.
Roskomnadzor also accused Google of censorship for allegedly restricting YouTube access to Russian media outlets, including RT and Sputnik.
"This censorship of Russian media and the targeted support for illegal protest activity actually speak to the political colouring of Google's activities in Russia," Roskomnadzor said.
Google's Russian arm last week lodged an appeal against a Moscow court order obliging it to unblock the YouTube account of a Christian Orthodox news channel owned by a Russian businessman who is under US and EU financial sanctions.
Moscow court documents also showed on Monday that Google was suing Roskomnadzor over the demands it removes banned content.
Roskomnadzor said the lawsuit concerned 12 YouTube links to "unlawful content" which involved encouraging minors to join unsanctioned protests in January when people across Russia took to the streets to support jailed Kremlin critic Alexei Navalny.
Navalny and his allies have used YouTube widely to air graft allegations against senior Russian officials and to organise their opposition activities.
The YouTube channel of the staunch critic of President Vladimir Putin has close to 6.5 million subscribers.
Google filed its lawsuit on April 23, documents from Moscow's Arbitration Court showed, but it was only accepted on May 11 after some administrative issues had been ironed out. A hearing is scheduled for July 14.
Google Russia declined to comment on the lawsuit.