The FSB said the charges related to Telegram's failure to remove material "used by Ukrainian special services and by terrorist and extremist organisations to prepare and co-ordinate acts of sabotage and terrorism, mass killings, and cyber-fraud operations within the Russian Federation".
Soon afterwards, Telegram's official account on X posted an image of Durov making an obscene gesture with his middle finger.
There was no other immediate comment from Durov or Telegram.
Telegram, an encrypted messenger app founded in 2013, says it has more than one billion users, and is widely used on both sides of the Russia-Ukraine war.
Russia has repeatedly tried to restrict Telegram's use in recent years, promoting its own state-backed MAX messenger service.
Yet state bodies including the Kremlin and the defence ministry continue to post to Telegram on a daily basis.
Durov, who was born in Russia but now holds Emirati and French passports, founded Russia's Facebook equivalent, VKontakte, before selling his remaining stake in 2014 amid pressure from Russian authorities.
French authorities are investigating Durov over allegations that Telegram failed to adequately counter criminal activity on the platform and did not sufficiently co-operate with law enforcement requests.
Durov denies wrongdoing.
The Russian announcement follows an official state newspaper reporting in February that Durov was under investigation in a terrorism-related case.
In April, Durov posted on Telegram that a summons for "Suspect PV Durov" had been delivered to an apartment in Russia where he lived 20 years ago.
"They must be suspecting me of defending Articles 29 and 23 of the Russian Constitution - which guarantee freedom of speech and the right to private correspondence. Proud to be guilty!" he wrote at the time.
Durov's whereabouts were not immediately clear.
A May 16 post on his Telegram channel suggested he was in Dubai.
On July 23 he posted that he was "very impressed with Georgia" and hoped to be "back very soon".
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