Trump asked Putin, who smiled and nodded along. Peskov says a formal invitation would be sent shortly.
Last November, Trump canceled a meeting with Putin at the G-20 in Argentina after Russian Federation seized two Ukrainian vessels and their crew members in the Sea of Azov, but the continued detention of those crew members does not appear to be deterring the leaders from meeting this time.
He also said they will be discussing trade and military. "We have a very, very good relationship".
The 94-year-old Democrat was speaking at a Virginia forum moderated by presidential biographer Jon Meacham, who asked how the USA should "deal with Russia" interfering in the country's ability to have "free and fair elections".
"If fully investigated, it would show that Trump didn't actually win the election in 2016", the former president said.
They later discussed trade and economic ties with members of their delegations, he said.
Donald Trump lightheartedly asked Russian President Vladimir Putin not to interfere in the upcoming U.S. election during a meeting at the Group of 20 summit, their first since Special Counsel Robert Mueller documented alleged Kremlin efforts to manipulate the 2016 vote.
But the intelligence agencies did not assess whether that interference had affected the election or contributed to Trump's victory, and no evidence has emerged that votes were changed improperly.
The European Commission president, Jean-Claude Juncker, said, in a more humourous putdown, that he could not be bothered to read Putin's remarks.
President Donald Trump says German Chancellor Angela Merkel is a "fantastic person" and he's "glad to have her as a friend".
The U.S. president also said he has not agreed to not impose further sanctions on Beijing.
Putin, who has highlighted national populist movements in Europe and America, praised Trump for trying to stop the flow of migrants and drugs from Mexico and told the newspaper that he thinks liberalism - the main political ideology in the West since the end of World War II - is dead.
Details of the Putin-Trump talks weren't immediately known.
(CNN)UK Prime Minister Theresa May and Russian President Vladimir Putin had a frosty meeting in Japan on Friday, when May asked for the Russian men that Britain blames for a high-profile poisoning to be brought to justice.
Japanese Prime Minister Shinzo Abe and his wife Akie Abe welcome US President Donald Trump.
Mr Trump and Mr Abe were later joined by Mr Modi and the portion of the meeting open to reporters was convivial: at Mr Trump's urging, the three leaders engaged in a group fist-bump.
His aides had grown anxious that Trump could use the meeting to once again attack the Russian Federation probe on the world stage, particularly since Mueller recently agreed to testify before Congress next month.
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