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, The Independent reports.
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.
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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.
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"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 organizations.
"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.”
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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.”
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.