Josep Borrell, the EU's foreign policy chief, said Russia's participation was suspended until the country "changes course".
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The EU has rejected the idea of inviting Russia back into the fold of meetings involving major world economic powers.
Moscow was suspended from what was then the G8 in 2014 after the annexation of Crimea.
US President Donald Trump said on Saturday that the make-up of the current G7 is "very outdated" and that he plans to invite Russia, Australia, South Korea and India to attend the next one.
Josep Borrell, the EU's foreign policy chief, said Russia's participation was suspended until the country "changes course".
Borrell said it was up to Trump as G7 chair to issue guest invites, saying that such invitations "reflect the host priorities".
But to change the membership or format on a permanent basis is "not the prerogative of the G7 chair".
The get-together of leaders from the US, Germany, France, Canada, Japan, Italy and the United Kingdom was initially planned for 10-12 June but has been delayed over coronavirus measures.