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The Russian Foreign Ministry said it had given notification of its departure to the Secretary General, Marija Pejcinovic Buric.
The decision ends Russia's 26-year membership of the Council of Europe and opens the way for Moscow to reimpose the death penalty if the authorities decide to do so.
Its departure from the council means Russia will no longer be a signatory to the European Convention on Human Rights.
Its citizens will no longer be able to file applications to the European Court of Human Rights.
Italian Foreign Minister Luigi Di Maio, the President of the Council of Europe's Parliamentary Assembly, Tiny Kox, and Ms Buric announced the Russian departure.
"As leaders of the Council of Europe we expressed on several occasions our firm condemnation of the Russian Federation's aggression against Ukraine," they said.
"The Committee of Ministers will hold an extraordinary meeting tomorrow morning in the light of today's notification by the Minister of Foreign Affairs of the Russian Federation of the Russian leadership's decision to withdraw from the Council of Europe."
Ukraine's Prime Minister Denys Shmyhal on Monday demanded that Russia be immediately expelled, saying it had no right to remain a member after sending troops to the pro-western country.
Dmytro Kuleba, the Ukrainian Minister of Foreign Affairs, said on Twitter that the Parliamentary Assembly of the Council of Europe "voted to withdraw Russia from the Council of Europe".
Mr Kuleba said it should have been done in 2014, the year Russia annexed Crimea.
"This is the Assembly that voted to return Russia not long ago," he tweeted. "Now it’s time for de-Putinisation. The final decision is up to the Committee of Ministers."
The Russian Foreign Ministry posted that it was "launching the procedure to exit the Council of Europe" on its Telegram account, saying it had "no regret" about leaving.
Russia joined the Council of Europe in 1996.
The ministry said its exit would "not affect the rights and freedoms of Russian citizens" and that "the implementation of already adopted resolutions of the European Court of Human Rights will continue, if they do not contradict Russia's Constitution".
It claimed that EU and Nato member states on the council had turned the organisation into an "instrument for anti-Russian policies".
Russia's exit will mark a major change for the ECHR which acts as a court of final instance when all domestic avenues are exhausted.
Cases brought by Russian citizens have piled up at the European court, accounting for 24 per cent of the current cases, such as those concerning dissident prisoner Alexei Navalny.
No member state has ever been expelled from the Council of Europe, which was created in 1949 and has 47 member states, including Russia.
Moscow's move has one precedent. Greece, under military rule, walked out in 1969 to avoid being expelled. Athens then rejoined in 1974 after the fall of the junta.
Not using the death penalty is a condition of membership, and former Russian president Dmitry Medvedev, now deputy national security council chief, suggested bringing back capital punishment if Russia left the body.
Mr Medvedev described Russia's suspension as "a good opportunity to restore a number of important measures to prevent especially serious crimes, such as the death penalty ... which is actively used in the US and China".
Russia has observed a moratorium on the death penalty since 1996 although it never formally abolished it.
Belarus, the only European country to still use the death penalty and Moscow's ally, is not a member of the organisation.
A Russian exit will also deprive the council of nearly 7 per cent of its annual budget, or about €500 million ($545m).
But Ms Buric told AFP this month she had received "reassuring" signals from member states, including France and Germany, ready to guarantee the organisation's financial sustainability.