Commenting on the G-7's statement, Putin said: "It's time to stop that chatter and deal with real issues".
Speaking from China where Putin was attending a regional security summit, Peskov said that in their last telephone conversation on March 20 the Russian and United States leaders had also mentioned possibly meeting in Vienna.
"President Trump has placed himself on the wrong side: with the autocrats, the corrupt, and the anti-Americans, who look to Vladimir Putin as a natural ally", said Daniel Fried, a former career diplomat who oversaw sanctions on Russian Federation after its Ukraine intervention.
Mr. Putin said last month that the proposed summit between him and Trump was not working out for now and was beset by problems.
"The (prime minister) has always said we should engage with Russian Federation but beware", the source told Reuters.More news: Taliban agree three-day Eid ceasefire in Afghanistan
US-Russian relations have been hit by years of disagreement over the Syrian conflict, Russia's annexation of Crimea and its involvement in eastern Ukraine.
Russia's President Vladimir Putin and Iranian President Hassan Rouhani met Saturday to discuss regional issues including both countries' involvement in the Syrian civil war and the USA withdrawal from a landmark nuclear deal with Iran.
The Chinese president even gave his Russian counterpart a large gold necklace-technically a "friendship medal"-as a symbol of their growing bond".
It can only be conferred on a foreigner who has made outstanding contributions in promoting exchange and cooperation between China and the world, and in maintaining world peace.
Its member states also include four former Soviet Central Asian republics, Pakistan and India.More news: EA announces Sea of Solitude
Vienna has been discussed as a possible venue for a summit between Vladimir Putin and Donald Trump, the Kremlin said Saturday.
Russian President Vladimir Putin also criticised the USA for its withdrawal, claiming the decision could potentially destabilise the situation.
Trump was due to arrive in Singapore on Sunday ahead of a historic summit with North Korean leader Kim Jong Un.
"I see this as an acknowledgement and an evaluation of Russia's efforts to develop a comprehensive strategic partnership with China", he said.
Xi also spoke of the increased number of visits from Chinese to Russia and also of Russians to China.
Russian President Vladimir Putin has criticized the US withdrawal from the Iranian nuclear deal in a speech at a regional summit in China.More news: Israeli troops kill 3 Palestinians, injure 600 along Gaza border: medics