Moscow was expelled from the club of the world's leading industrial nations in 2014 after annexing Crimea from Ukraine, but Trump says the current membership is "outdated".
Trump said on Saturday he would delay the summit scheduled for this month and invite other countries, including Russia, to join the meeting.
But EU foreign affairs high representative Josep Borrell said that Russia had not changed course since 2014 and so should not be re-admitted.
"The prerogative of the G7 chair, in this case the United States, is to issue guest invitations -- guest invitations reflect the host's priorities," Borrell said.
"But changing membership, changing the format on a permanent basis, is not a prerogative of the G7 chair."
Leaders from the Group of Seven -- the US, Britain, Canada, France, Germany, Italy and Japan -- had been scheduled to meet by videoconference after coronavirus scuttled plans to gather in-person at Camp David, the US presidential retreat outside Washington.
Canadian Prime Minister Justin Trudeau rejected the idea of inviting Russian President Vladimir Putin, citing his "continued disrespect and flaunting of international rules and norms". (AFP)