Putin said that Moscow would support full-fledged Iranian membership in the group.
Reports said the Kremlin has reached out to Austria about hosting a meeting between Trump and Putin sometime this summer.
Mr Putin arrived for a three-day state visit during which he will attend the Qingdao Summit of the Shanghai Cooperation Organisation on the weekend.
"President Putin and I both think that the China-Russia comprehensive strategic partnership is mature, firm and stable", Xi told reporters after their meeting.
Stressing that Russia-China comprehensive strategic partnership of coordination remains Russia's diplomatic priority, Putin said the two countries have taken care of each other's core interests and major concerns, actively promoted dialogues and cooperation in political, economic and people-to-people and cultural areas, and worked closely in global affairs.
Mr Putin said last night he thought it was important the two men meet and said he shared Mr Trump's concerns about the risks of an arms race developing between Russian Federation and the US. He added that Russian Federation would seek to maintain the agreement despite U.S. plans to resume sanctions against Iran. According to White House statements, Trump last spoke to Putin on March 20.
"The US president himself repeatedly said that he would consider such a meeting helpful". However, having pulled out of the deal, the USA now says it will impose severe economic and trade sanctions on Iran.
"We have been a faithful player to this commitment, we've done our best, we've shown our good intentions". Russian Federation was kicked out of the G7 after it annexed Ukraine's Crimea in 2014.
President Donald Trump doubled down on his suggestion that Russian Federation be re-admitted into the G-7 in an impromptu presser on Saturday morning from the summit in Canada.More news: Nadal Wins 11th French Open Title
Italy's new prime minister, Giuseppe Conte, seconded Trump's idea.
Putin also said he would be happy to welcome the leaders of G7 to Moscow any time.
"Both share scepticism towards American hegemony and distrust United States intentions, both are authoritarian personalistic rulers", he said.
Earlier on Sunday, Putin criticised the United States withdrawal from the Iranian nuclear deal in a speech at the summit.
The Kremlin leader did not miss an opportunity to thumb his nose at the club of leading industrialised democracies, saying that the combined purchasing power of the Shanghai Cooperation Organisation -which includes Russian Federation and China - outstripped the G7.
"The recent example of such unilateralism and the defiance of the decisions of the global community by the USA government is its withdrawal from the JCPOA", he said, referring to the nuclear agreement by its official name, the Joint Comprehensive Plan of Action.
Putin also lambasted Trump's decision to withdraw from the 2015 Iranian nuclear deal, saying the decision could "destabilize the situation" in the region.