"We've had really a very good relationship, very special", the USA president said of Macron, a day after the two leaders had exchanged terse messages on Twitter.
Mr Putin spoke during a meeting ahead of a summit in Beijing featuring their two countries and six Asian states. But after Russia's intervention in Ukraine and annexation of Crimea, Western leaders sought to isolate Vladimir Putin's government.
The suspension was supported by the other members of the group, including the US, Canada, Japan and four European nations. Trump has said he was open to having a summit with Putin, who United States intelligence officials have said directed Russian meddling in the 2016 election to help Trump win. "I would recommend, and it is up to them, but Russian Federation should be at the meeting", Trump noted.
The annual G-7 summit appeared to have weathered tensions over President Donald Trump's threats of a trade war.
Macron said, in part, "sometimes we disagree but we always speak and share I think common concerns and common values, and we share a willingness to deliver and get results together".
"We have a world to run", Trump said.
It's revealing that he said "we should have Russian Federation at the negotiating table", because the G-7 meeting is not a negotiation.
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Under the plans agreed by the UK, US, France, Germany, Canada, Italy and Japan at the summit in Quebec, there will be greater co-ordination to identify and respond to threats including cyber attacks and other breaches of worldwide rules.
Pakistani President Mamnoon Hussain and the prime minister of arch-rival India, Narendra Modi, are also in attendance.
Russian Federation and China have responded to the United States national security strategy describing them as America's top adversaries by vowing to further expand their economic, political and military co-operation.
In response, Macron said in a statement France would stand by the G-7 joint communiqué - which includes a pledge by the seven leading industrialized democracies to "continue to fight protectionism" - despite Trump's refusal.
"As for Russia's return to the G7, or G8: we did not leave it".
Trump's remarks were the latest show of disunity between the US and the other six nations meeting at a resort on the Saint Lawrence River this weekend.
Trump also lashed out at longtime allies over their criticism of his trade policies.
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Cory Gardner, R-Colorado, told reporters that military exercises "will continue with South Korea " despite the president's remarks.
The premier, however, said that Britain had registered its "deep disappointment at the unjustified decision by the U.S.to apply tariffs to European Union steel and aluminum imports" at the meeting.
Referring to the Mueller investigation, and the possibility it may result in criminal charges against him, Trump maintained he has "the absolute right to pardon myself", adding "but I'll never have to do it because I didn't do anything wrong".
The president reiterated the idea that a trade agreement could take a different shape, namely, individual deals with Canada and Mexico.
Asked in Qingdao about the G-7's tumultuous meeting Friday and Saturday in Canada, Putin focused on the rift between Europe and the United States on tariffs, which he said "is more significant than any emotional outbursts".
Previous G7 summits have seen large-scale anti-globalization protests, but Trump was a main target of the demonstration as masked anarchists set fire to USA flags and those of other G7 nations.
But to Trump, the very idea of global cooperation is anathema.
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