Russia was expelled after its annexation of Crimea in 2014
US President Donald Trump has called for Russia to be readmitted as a member of the G7 group of industrialised nations.
The country was expelled from what was then called the G8 after it annexed Crimea, but Trump said it should now come back.
He found support in Italy's new prime minister Giuseppe Conte, who tweeted that it was "in the interests of everyone" for Russia to be readmitted.
The G7 in Canada was also an opportunity for Conte to meet EU leaders for the first time.
Donald Tusk, the European Council President, said he had a "very good meeting, very promising meeting".
He added: "I'm convinced that here at the G7 we will have a fully united European position on all issues, including on Russia. I'm talking not about details but about the more general, common line."
A Russian government source appeared to snub Trump's proposal.
"Russia is focused on other formats, apart from the G7,"Kremlin spokesman Dmitry Peskov said in a brief statement reported by the government-controlled Sputnik news agency.
A senior British government source told Reuters that Russia needed to change its approach before any conversation about it rejoining the G7 could begin.
Meanwhile, a source close to the French President Emmanuel Macron said Trump's proposal did not seem "coherent" in view of the latest economic sanctions imposed by the United States on Moscow.