Moscow said it had no intention of re-joining the influential bloc – which brings together the world’s richest countries to discuss global issues from economic growth to terrorism - even if it was invited to do so.
Russia’s involvement in the G8 was “not being discussed in Moscow in any way", said Kremlin spokesman Dmitry Peskov.
The country was temporarily suspended from the bloc – which includes the UK, US, France, Germany, Italy, Japan and Canada – in March 2014. Since then, the G7 has met in its place.
At the time US President Barack Obama’s security adviser said there was “no need for the G7 to engage with Russia” while Moscow continued to violate international law.
Announcing Russia's intention to leave permanently, Mr Peskov said Vladimir Putin’s priority was now the G20 - a much wider group of countries which includes emerging economies such as Brazil and Mexico as well as Turkey and Saudi Arabia.
He said: “We’ve not heard the heads of state that keep gathering for G7 meetings ever say anything that might sound like an intention to invite Russia or some other countries.
"As far as Russia is concerned, regardless of any eventual proposals and invitations, Russia’s priority is participation in the G20.
"The Russian president has said this more than once.”
Russian Prime Minister Dmitry Medvedev went further and suggested the G7 and G8 were now defunct political organisations.
"The G20 format actually replaced the G7 and G8 groups," he said. "It is clear what this Group of Seven means without other major economies. Nothing.”
He also hinted that Russia may try and forge new links with other nations that may exclude the traditional Western power brokers.
Mr Medvedev said: “We are determined to develop international trade, establish our own value chains and be more actively involved in international business alliances and agreements.”
However, Italy’s foreign minister attempted to strike a more conciliatory tone earlier in the week, saying he hoped Russia would soon re-join the G8.
Including Russia in the bloc would reduce East-West tensions and help end “the atmosphere of the Cold War”, Angelino Aliano said.
The next meeting of the G7 will take place in Italy on 26 May, three years after the last scheduled G8 meeting was cancelled months before it was due to be held in the Russian Black Sea resort of Sochi.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies