On the second day of the summit, Trump again called for Russian Federation to rejoin the group, downplaying the country's invasion of Ukraine.
The Wall Street Journal also reported earlier this month that the USA ambassador to Russia, Jon Huntsman, had come to Washington to meet with Trump administration officials to help arrange the meeting.
Russian Federation was expelled from what was then the Group of 8 (G8) in 2014 over its military seizure of Crimea and backing of armed separatists in eastern Ukraine.
Moscow does not rule out a meeting between Putin and Trump this summer, RIA news agency reported on Friday, citing Kremlin spokesman Dmitry Peskov. Then Trump argued Obama was asleep at the wheel when the intelligence community warned him about Russia's attempts to influence the 2016 election.
When asked more broadly whether Trump has a positive relationship with Putin, 60 percent of voters agreed compared to 25 percent who said the president did not have good relations with Russia's president.
Initially, the USA administration, then headed by President Bill Clinton, believed inviting Russian Federation to join in 1997 would encourage the post-Soviet leader, Boris Yeltsin, to approach the ideals of developed democracies with greater optimism and compliance.
The 44th annual summit was held between the seven G7 member states - Canada, France, Germany, Italy, Japan, the United Kingdom, the United States, and the representatives of the European Union - on June 8-9, 2018.
"Just so you understand, President Obama lost Crimea, just so you understand", he said. President Obama lost Crimea, because President Putin didn't respect President Obama, didn't respect our country, and didn't respect Ukraine.
But President Obama when he didn't go across the red line, what he gave away nobody even knows, he alleged.
He stated, "What Trump says is just as important as what he doesn't say".
Trump has been criticised for his outreach to Russia, particularly after the Obama administration severed US-Russian ties following Putin's annexation of Crimea.