Commenting on the G-7's statement, Putin said: "It's time to stop that chatter and deal with real issues".
Speaking in China, where Putin was attending a regional security summit, Russian presidential spokesman Dmitry Peskov told reporters that the two presidents discussed "the need for such a meeting" and the possibility that it could take place in the Austrian capital in their most recent phone call.
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.
The statement made no mention of Russian Federation being invited back into the group from which it was kicked out in response to its 2014 annexation of Crimea, despite US President Donald Trump's insistence that the club would be better off if it brought Russian Federation back into the fold.
Xi and Putin and others pledged their support of the Joint Comprehensive Plan of Action, the 2015 Iranian nuclear deal from which President Donald Trump withdrew the USA last month.
"Whether you like it or not, and it may not be politically correct, but we have a world to run", Trump said.
Both he and Mr Xi also held talks in the Chinese capital, where they hailed the close ties between their countries and discussed the upcoming US-North Korea summit, as well as the Iran nuclear deal.
Putin said the bloc's new counterterrorism agreement foresees joint drills, exchanging information and conducting coordinated anti-terror action.More news: MIT researchers use Reddit to create the first 'psychopath AI'
Xi placed the large golden medal around Putin's neck at the grandiose Great Hall of the People in Beijing in front of dignitaries from both countries.
Its member states also include four former Soviet Central Asian republics, Pakistan and India.
Putin also hit Trump on Sunday for his decision to withdraw from the Iran nuclear deal earlier this year. In general, I believe it is a technical issue.
Russian Federation and China "are interested in establishing peace and stability on the Korean peninsula", Putin said in a joint press briefing with Xi after their talks.
Putin, however, voiced his support for Trump's summit with North Korean leader Kim Jong Un in Singapore on Tuesday.
Xi later called Putin "my best, most intimate friend", which is not an endearment any western leader is likely to give Russia's autocratic leader.
Iranian President Hassan Rouhani walks to his auto after walking out from the airplane upon his arrival at Qingdao Liuting International Airport, Shandong province, China, June 8, 2018.
Last year Putin awarded Xi the Order of St Andrew for his distinguished service to the peoples of China and Russian Federation.