Trump has said he was open to having a summit with Putin, who U.S. intelligence officials have said directed Russian meddling in the 2016 election to help Trump win.
But Trump on Friday called on world leaders to allow Russian Federation back into the G7, the group of leading industrialized democracies.
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.
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.
Russian President Vladimir Putin too sounded critical of the USA decision, saying the move may destabilise the Gulf region.
Founded in 2001, the SCO also includes the former Central Asian Soviet republics of Kazakhstan, Kyrgyzstan, Tajikistan and Uzbekistan.
Rouhani also stressed the importance of developing bilateral cooperation in the fields of culture, science and technology and expressed hope that the Chinese government would facilitate issues for Iranian businessmen and students including in the banking sector.
Before the medal ceremony, Putin said the two heads of state had enjoyed "fruitful" talks. I think it would be good the United States.
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"As soon as the US side is ready, the meeting will take place, depending, of course, on my working schedule".
Trump has drawn frequent criticism for his friendly tone toward Russian Federation and Putin.
Coming in the shadow of the G7, the emphasis of Putin's visit is to deepen the political and economic partnership, and this trip has the bonus of meeting fellow SCO leaders from Kazakhstan, Kyrgyzstan, Russia, Tajikistan, Uzbekistan, India and Pakistan, and the observer states of Afghanistan, Belarus, Iran, and Mongolia.
"I think it would be an asset to have Russian Federation back in".
He added, however, that no concrete agreements have been reached and no concrete discussions were underway. "We will suspend our participation in the G-8 until Russian Federation changes course and the environment comes back to where the G-8 is able to have a meaningful discussion" the leaders wrote in The Hague Declaration in March 2014.
President Mamnoon Hussain on Saturday held a bilateral meeting with his Iranian counterpart President Hassan Rouhani and discussed relations between the two countries and the prevailing situation in the region, said a statement.
He once again slammed Washington for its illegal decision to withdraw from the internationally recognized accord.
He added: 'We will be ready to greet them all in Moscow'.
Xi and Putin also vowed to make "all possible efforts" to preserve the 2015 global accord on Iran's nuclear programme that Trump abandoned last month.
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