Russia was expelled in 2014 following its annexation of Crimea, but Mr Trump said he wanted them there.
The build-up to the meeting has been marred by clashes 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.
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.
Arriving at the summit, Mr Trump said he regretted the meeting had shrunk in size – potentially putting him at odds with other members on 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.
Source – BBC