But in Washington the director of the CIA said he stood by the US intelligence community's assessment that Russia did try to meddle in the election.
Trump, whose key former aides are under US investigation for possible collaboration with the Kremlin, said he repeatedly asked Putin about the claims during their chats at the APEC summit in the Vietnamese resort of Danang.
"He (Putin) said he didn't meddle. I asked him again," Trump told reporters on Air Force One as he flew to Hanoi for a state visit.
"I really believe that when he tells me that, he means it," added Trump, who is marking one year since his shock election victory.
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In May, US intelligence chiefs told Congress that they agreed with their analysts' conclusion that Russia had meddled in the election.
And in January, 17 US intelligence agencies took the extraordinary step of stating publicly that they believed Russia did try to interfere in the election.
"The Director stands by and has always stood by the January 2017 Intelligence Community Assessment entitled: Assessing Russian Activities and Intentions in Recent US Elections. The intelligence assessment with regard to Russian election meddling has not changed," the statement reads.
The US president's latest comments suggest he accepts Russia's staunch denials that the Kremlin played no part in helping him get to the White House -- allegations that continue to dog Trump's administration.
US Democratic lawmakers criticized Trump harshly for his statement.
Schiff said Trump understands the Russians hacked into Democratic leaders' emails and dumped them, and used social media in a bid to hurt Hillary Clinton and help him win the election and divide the country.
"He understands all this and more," Schiff said in a statement. "He just doesn't understand how to put country over self. Or to put it in terms he is more familiar with - Mr. Trump simply can't bring himself to put America first."
Putin also addressed the allegations on Saturday after his meeting with Trump, describing them as a US "domestic political struggle."
Trump's former campaign chairman Paul Manafort and an associate are under house arrest on charges unrelated to the election which were brought by special counsel Robert Mueller, who is investigating the allegations that the Trump campaign colluded with Russia.
Revelations by Facebook and Twitter that Russian- sponsored fake news flooded US social media during the election run-up have further deepened scrutiny on ties between the nations.
Trump and Putin met three times on the margins of the APEC summit, sharing warm handshakes and brief words.
The pair appeared to have struck a chummy tone, with Trump describing a "very good feeling" after the talks, and Putin remarking on the "well-mannered" former reality TV star.
"Look, I can't stand there and argue with him," Trump said. "I'd rather have him get out of Syria, I would rather get to work with him on the Ukraine."
The exchanges produced a rare common ground on the war in Syria, a bloody six-year conflict which has seen the US and Russia back competing factions.
In a joint statement, the leaders said there was "no military solution" to the war, an agreement that may mark a small step toward peace.
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