The group, which involves many of the richest economies in the world, were known as the G8 until Moscow was expelled.
Upping the drama as he set off for the 47th meeting of the group in Canada, Mr Trump told reporters as he left the White House it would be better if Moscow was also at the annual summit. “Why are we having a meeting without Russia in the meeting,” he said. “They should let Russia come back in because we should have Russia at the negotiating table.”
He added: ”I have been Russia’s worst nightmare, but they should have been invited.”
Mr Trump’s suggestion received mixed early reactions from other members of the world’s top economies. Italian prime minister Giuseppe Conte said he supported Russia’s readmission to the group, while Canada said its opposition to the idea had not changed.
“I agree with President (Trump). Russia should be re-admitted into the G8. It is in the interests of everyone,” said Mr Conte said in a tweet from Canada, where he is due to make his international debut as Italian leader at a summit of world power leaders.
Reuters quoted a French presidential source as saying Mr Trump’s opinion did not seem “coherent” in view of the latest sanctions imposed by the US on Moscow.
And the Russian government itself appeared to snub Mr Trump's idea.
"Russia is focused on other formats, apart from the G7," Kremlin spokesman Dmitry Peskov said in a brief statement reported by the government-controlled Sputnik news agency.
“As a reminder, the latest country to have imposed individual economic sanctions is the United States, so this proposal doesn’t seem coherent,” the Elysee source added.
President Emmanuel Macron’s aim is to present a united European front at the G7, the source said, adding that he aimed to get references to international trade rules, WTO reform, the Paris climate agreement in the final statement, as well as to reach consensus on Iran and Libya.
The Italian government, backed by the anti-establishment 5-Star Movement and far-right League, has already signalled it is likely to adopt a pro-Russian line in its foreign policy and has called for an end to economic sanctions on Moscow.
Mr Trump’s injection of drama as he set off for La Malbaie, in Quebec, came he prepared for difficult meeting with allies such as Britain and Canada, who are furious over his decision impose tariffs on imports of steel and aluminium. Both countries – along with Mexico and the EU – had lobbied hard for an exception to the tariffs.
Russia was ousted from the elite group in 2014 as punishment for President Vladimir Putin’s annexation of Crimea and its support for pro-Russian separatists in Ukraine.
In the US, special counsel Robert Mueller is investigating whether Trump’s campaign colluded with Russia in a bid to sway the 2016 presidential election in his favour.
The Associated Press said Mr Trump will arrive Friday at the annual gathering, held this year at a Quebec resort, but will leave Saturday morning before the event is over, heading to Singapore for his much anticipated summit with North Korean leader Kim Jong Un.
The White House announced his travel plans after French President Emmanuel Macron and Canadian Prime Minister Justin Trudeau signalled they would use the G7 event to take a stance against new US tariffs on steel and aluminium imports. Indeed, it seems likely that he may personally miss those negotiations as he will have left for south east Asia.
“Looking forward to straightening out unfair Trade Deals with the G-7 countries,” Mr Trump tweeted early on Friday. “If it doesn’t happen, we come out even better.”
Mr Trump also singled out tariffs on US. dairy products in yet another scathing tweet directed at Canada just before the G7.
At a joint press conference on Thursday, Mr Macron said: “A trade war doesn’t spare anyone. It will start first of all to hurt US workers.” In turn, Mr Trudeau said: “We are going to defend our industries and our workers.”
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