Discussion on "solving the Korean Peninsula's nuclear problem" must involve the lifting of sanctions on North Korea, Lavrov told his North Korean counterpart Ri Yong Ho before meeting Kim, Russia's state-run Tass news service reported.
Russia was ousted from the elite group - then known as the G8 - in 2014 as punishment for Russian president Vladimir Putin's annexation of Crimea and its support for pro-Russian separatists in Ukraine.
Following a formal welcoming ceremony at the Great Hall of the People in central Beijing, Putin first with Premier Li Keqiang, telling him that Russia-China trade and economic ties have "gained a good tempo, and we are looking for new spheres of cooperation".
Trump's presidency has been clouded by a federal investigation into alleged Russian meddling in the 2016 presidential election, and possible collusion by his campaign. If Hillary got in, I think Putin is probably going, 'Man I wish Hillary won, ' because you see what I do.
"We share and agree with the United Kingdom's assessment that it is highly likely that the Russian Federation was responsible for the attack, and that there is no plausible alternative explanation", the G7 statement said.
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 global rules.
He also blamed ex-President Barack Obama for the annexation of Crimea by Russian Federation. "We have opened both our country and our hearts to the world".
US President Donald Trump steps off Air Force One upon arrival at Palm Beach International in West Palm Beach, Florida on April 18, 2018.
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Putin's comments come as Trump's relations erode with key allies, including lashing out Saturday at Canadian Prime Minister Justin Trudeau, who expressed opposition to Trump's trade policies at the conclusion of the summit in Canada.
But this apparently spontaneous suggestion - rejected out of hand by the other allies - did not make it to the summit table, where instead the leaders confronted Trump's assault on the world trade system.
The White House says President Donald Trump will deliver a statement before departing a meeting of industrialized nations in Canada.
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.
"As soon as the American side is ready this meeting would take place depending on my working schedule of course", Putin told reporters in the Chinese city of Qingdao.
G7 chiefs have largely praised Trump for his efforts to stabilise the Korean peninsula, but they are unhappy he pulled out of an worldwide agreement to limit Iran's nuclear ambitions.
In an effort to counter propaganda, the G7 leaders agreed to work together to assert a "common narrative and response" to incidents.
The president tweeted that he was heading for Canada "for talks that will mostly center on the long time unfair trade practiced against the United States".
"Our relationship is very good".