Putin said he is seeking to meet with President Trump to discuss the threat of a new arms race, as well as several other foreign affairs issues.
Trump's call also comes amid the continuing criminal and congressional investigations into what the USA intelligence community concluded was a campaign by Moscow to use propaganda and hacking to influence the 2016 US presidential election.
'As soon as the USA side is ready, the meeting will take place, depending, of course, on my working schedule'.
President Xi Jinping gave the leaders of Pakistan and India a "special welcome" to their first summit of the Shanghai Cooperation Organisation (SCO), in the eastern Chinese city of Qingdao, since their countries joined the group past year.
Lawmakers in the United States have condemned Trump's comments, which some have taken as the latest example of the US President's failure to condemn Russian Federation for its interference in the 2016 election.
Putin's latest trip has emphasised the positive mood music between the Russian and Chinese presidents which is underpinning the wider warming of ties. "We focus on other formats", TASS quoted Putin's spokesman Dmitry Peskov as saying.
Both the countries also underscored that they were ready to join their efforts to bring bilateral relations to a new, higher level.
GETTYUS President Donald Trump said he will soon invite PM Conte to the White House
In April, the White House confirmed that Trump and Putin discussed the possibility of meeting at the White House "in the "not-too-distant-future" during a phone call the previous month.
"This medal of friendship represents the Chinese people's lofty respect for President Putin, and symbolizes the profound friendship between China and Russian Federation", he said.
He said: "I've always said that our country must remain within North Atlantic Treaty Organisation, but the sanctions are damaging us".
"We (have) always been clear we should engage with Russian Federation where it is in our interests, but we need to remember why G8 became the G7, it was because Russian Federation illegally annexed Crimea", a European diplomat said Friday. Putin added that a thorough discussion is needed to address the issue.
Highlighting the importance of maintaining regional stability and security, he added, "we want to see a secure and stable Afghanistan, and the coordination of Iran, Pakistan and Afghanistan is very important for the security and development of the region".
Trump had said Saturday that re-admitting Russian Federation to the elite club would be "an asset", telling reporters, "We're looking for peace in the world".
"The very fact that we confirm the high level of our interaction and talk about the need for its development, in my opinion, is of great importance, for contemporary global relations, for Russian-Chinese relations", he said. He also blamed former US President Barack Obama for Russia's move into that nation.
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