US President Donald Trump says he wants Russia to be part of the G7 group of key industrialised nations.
Russia was expelled in 2014 following its annexation of Crimea, but Mr Trump said he wanted the country readmitted.
The build-up to the meeting has seen major disagreements between the US president and other nations over his imposition of trade tariffs.
There are also likely to be disagreements with Mr Trump over Iran and climate change.
A looming row over trade
Why this could get awkward
What is a trade war?
How allies are retaliating against Trump
The G7 summit, which groups Canada, the US, the UK, France, Italy, Japan and Germany, is being held in the town of La Malbaie in Quebec, Canada.
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.
What did Mr Trump say about Russia?
Mr Trump said he regretted the meeting had shrunk in size, putting him at odds with most other G7 members on yet another issue.
"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," he said.
He found support in the shape of the newly installed Italian Prime Minister Giuseppe Conte, who tweeted that it was "in the interests of everyone" for Russia to be readmitted. But Canada, France and the UK immediately signalled they remain opposed.
Fellow members of what was then the G8 suspended Russia after it took control of Crimea, saying it would remain until Russia "changes course".