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.
The BBC reports that there are also likely to be disagreements with Mr Trump over Iran and climate change.
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.