The spokesman for the Kremlin Dmitry Peskov told reporters that the summit had helped to reduce tensions on the Korean Peninsula.
Mr Trump phoned South Korean president Moon Jae-in after leaving Singapore to brief him on the discussions.
Last week Russian Federation invited the North Korean dictator to visit the country and it is believed Kim may do so during an economic forum in September.More news: Trump Slams Robert De Niro as 'A Very Low IQ Individual'
Earlier Wednesday, North Korea's state KCNA news agency said denuclearization would be a "step by step process" with "simultaneous action", a stance that appeared to contradict the US refusal to offer sanctions relief before North Korea gives up its nuclear weapons.
"Under the circumstances that we're negotiating a very comprehensive complete deal, I think it's inappropriate to have war games", Trump said of the joint military exercises that for decades have bolstered USA and South Korean readiness.
Bother U.S. allies view the drills as a bulwark against North Korean aggression and necessary to ensuring a stable security architecture in Northeast Asia.
On Tuesday, Trump and Kim signed a statement outlining four points, including reaffirming a commitment to denuclearize the Korean peninsula. Fears of conflict were particularly acute after Trump called Kim "Rocket Man" and Kim pledged to "tame the mentally deranged USA dotard with fire". "No longer - sleep well tonight!" the President wrote. -South Korea war games as part of the negotiations with Kim.
Independent experts say the North could have enough fissile material for anywhere between about a dozen and 60 nuclear bombs. -South Korean drills was met with concern.More news: KKR Nears Agreement to Acquire Envision for about $5.5B
USA soldiers stand guard near a U.S. F-22 stealth fighter at the Osan Air Base on February 17, 2016 in Pyeongtaek, South Korea. "They are fighting hard to downplay the deal with North Korea".
Mr Trump repeatedly praised Kim's negotiating skills and their new relationship and expressed hope for "a bright new future" for Kim's impoverished nation. The report said Kim told Trump "that it is urgent to make bold decision on halting irritating and hostile military actions against each other". And Secretary of State Mike Pompeo sought to keep expectations for the summit in check.
"It will include identifying all sites used for research, development, production, testing and deployment of various weapons systems, and then it will include designing a protocol for verifying the stopping or destruction of facilities", Dill said. Pompeo is also due to meet the South Korean and Japanese foreign ministers. Mr Pompeo, the former Central Intelligence Agency director, then plans to fly to Beijing to update the Chinese government on the talks.
On Monday, Mattis told Pentagon reporters that there had been no discussions on future withdrawals of US troops from Korea.More news: Californians to vote in November on breaking into 3 separate states
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