"Every time he sees me he says, 'I didn't do that, ' and I really believe that when he tells me that, he means it", Trump told reporters following the meeting. "It has enormous importance for Russian Federation and America, but it [also] has huge importance for the whole worldwide situation. I think it will be the main worldwide event of the summer".
Moscow and Washington will announce the time and place of the summit on Thursday.
The U.S. government does not plan to recognize Russia's annexation of the Crimean peninsula from Ukraine, National Security Adviser John Bolton confirmed during a press conference in Moscow on Wednesday.
The Kremlin spokesman would not disclose the agenda of the meeting and declined to specify whether it will be part of preparations for potential bilateral negotiations between Putin and US President Donald Trump.
Saying he wanted to find areas where the two countries could agree, Bolton also praised Russia's hosting of the 2018 soccer World Cup, while Putin congratulated the United States on winning the right to jointly host the 2026 tournament.
Some Trump critics in Washington has expressed concern that, in his eagerness to come back from a summit with a "deal", Trump might concede too much to Putin without getting much in return.
"It was stated clearly by our side that the Russian state hasn't interfered with the USA domestic politics, moreover hasn't interfered in the 2016 election", Ushakov said. "Russia has never sought confrontation".
U.S. officials have proceeded as if Trump will meet Putin in mid-July after stops in Brussels for the North Atlantic Treaty Organisation talks and Britain for a working visit.
The news of this exchange was made all the more piquant by Mr Bolton's Daily Telegraph article past year saying that Mr Putin had lied to Mr Trump about the election meddling, which Mr Bolton called an "act of war".
He added that when Moscow and Washington had differences in the past, Russian and USA leaders still met.
Since then, already poor ties between Washington and Moscow have deteriorated further over the conflict in Syria and the poisoning of a former Russian spy in Britain which sparked big diplomatic expulsions in both countries.
The discussions touched on the state of bilateral ties, nuclear arms control, the situation in Syria, the Ukrainian crisis, developments around North Korea and the USA exit from the Iranian nuclear deal - topics Ushakov said would shape the summit agenda. He said he did not rule out Trump discussing Russian Federation rejoining the G7 to make it the G8 again.
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He also praised Bolton, who joined the administration in April, for traveling to Moscow in the interest of restoring relations.