President Donald Trump, who is attending the G7 summit in Canada, says Russia should be part of the group.
Russia was expelled in 2014 following its annexation of Crimea, but President Trump said he wanted the country readmitted.
Fellow members of what was then the G8 suspended Russia after it took control of Crimea, saying it would remain until Russia “changes course”.
The build-up to the meeting has seen major disagreements between President Trump and other nations over his imposition of trade tariffs.
There are also likely to be disagreements with the US president over Iran and climate change.
The G7 summit, which groups the US, the UK, Canada, France, Italy, Japan and Germany, is being held in the town of La Malbaie in Quebec.
The leaders of the nations, which represent more than 60% of global net worth, meet annually. Economics tops the agenda, although the meetings now always branch off to cover major global issues.
President Trump said he regretted the meeting had shrunk in size, putting him at odds with most other G7 members on yet another issue.
He said: “You know, whether you like it or – and it may not be politically correct – but we have a world to run and in the G7, which used to be the G8, they threw Russia out. They should let Russia come back in.”
President Trump found support in the shape of the newly installed Italian PM Giuseppe Conte, who tweeted that it was “in the interests of everyone” for Russia to be readmitted.
Canada, France and the UK though immediately signaled they remain opposed to Russian re-entry. A Kremlin spokesperson said they were interested in “other formats”, apart from the G7.
Russia’s President Vladimir Putin is currently in Beijing, where he was presented with a friendship medal by Chinese counterpart Xi Jinping.