Speaking at a news conference in the Vietnamese capital, Trump was clarifying remarks he made a day earlier which suggested Putin was being sincere in his denials that Moscow engaged in election meddling.
The President stressed he was not accepting Putin's denials at face value, instead saying he merely believed Putin was being genuine.
"I believe that he feels that he and Russia did not meddle in the election," Trump said. "As to whether I believe it or not, I am with our agencies, especially as currently constituted with the leadership."
Trump has long declined to say definitively whether he believes Russia was behind the attempts to sway last year's election. And he did not say conclusively on Sunday when asked directly whether Russia was responsible. But his nod toward American intelligence agencies, which he said were led by "very fine people," put him closer to accepting what his own government has determined happened months ago.
The remarks came after Trump ignited further controversy over the Russia interference issue when he told reporters aboard Air Force One on Saturday that he believed Putin was being sincere when he denied involvement in the cyber-intrusion.
"I really believe that when he tells me that, he means it," Trump said.
Backlash in Washington
The remark prompted backlash in Washington, where intelligence officials are unanimous in their assessment that Russia sought to influence last year's contest.
The CIA released an unusual statement saying the current director Mike Pompeo believes the agency's determination that Russia was behind the election meddling.
Trump, however, insisted during his news conference on Sunday that his remarks were clear.
"I'm surprised there's conflict on this," he said. "I think it was very obvious to everybody."
Trump said he didn't want to engage in a public spat with his Russian counterpart over the issue of election meddling during talks this week in Vietnam.
"I'm not looking to stand and start arguing with somebody when there are reporters all around and cameras recording and seeing our conversation," Trump said.
His meetings with Putin in Da Nang were held in private, however, and reporters did not see the two men engage in discussions.
Trump said it was imperative the US and Russia work together to solve problems like Syria and North Korea.
"What I believe is we have to get to work," Trump said. "People don't realize, Russia has been very, very heavily sanctioned. They were sanctioned at a very high level. And that took place very recently. It's now time to get back to healing a world that is shattered and broken."
Earlier Sunday, Trump unleashed a series of tweets as he nears the end of his epic 13-day diplomatic tour of Asia, going after "haters and fools" who question his ties to Russia and mocking the shape of North Korean dictator Kim Jong Un
The stream of invective came after days of relatively restrained tweeting as Trump darted between Asian capitals on his first presidential trip to the continent.
"When will all the haters and fools out there realize that having a good relationship with Russia is a good thing, not a bad thing," Trump wrote at 7:18 a.m. local time in Hanoi.
He spent the night here after a state dinner, and held talks and a joint news conference with Vietnamese President President Tran Dai Quang on Sunday morning.
"There (sic) always playing politics - bad for our country," he added. "I want to solve North Korea, Syria, Ukraine, terrorism, and Russia can greatly help!"
In a second posting at 7:43 a.m., Trump wrote: "Does the Fake News Media remember when Crooked Hillary Clinton, as Secretary of State, was begging Russia to be our friend with the misspelled reset button? Obama tried also, but he had zero chemistry with Putin."
He was referencing a 2009 episode in which Clinton, then secretary of state, presented her Russian counterpart, Sergey Lavrov, a small red button with the Russian word "peregruzka" printed on it.
"We worked hard to get the right Russian word. Do you think we got it?" she asked Lavrov, laughing.
"You got it wrong," said Lavrov. The correct word for "reset" was "perezagruzka," he explained. "Peregruzka" means "overcharged."
Trump has long insisted that a better relationship with Russia could help solve vexing global problems, including ending the civil war in Syria and containing North Korea.
Trump has worked while in Asia to consolidate support behind his efforts to choke off support for Pyongyang, and delivered stern warnings to Kim during stops in Tokyo and Seoul.
But his message on Twitter Sunday delved further into the types of personal insults that colored his rhetoric about the dictator before arriving in Asia.
"Why would Kim Jong-un insult me by calling me 'old,' when I would NEVER call him 'short and fat?'" Trump wrote at 7:48 a.m. "Oh well, I try so hard to be his friend - and maybe someday that will happen!"
He appeared to be responding to North Korea's statement last week that Trump is a "dotard," implying senility.
Asked at his news conference about the prospects of befriending Kim, Trump offered a coy response.
"Strange things happen in life," he said. "That might be a strange thing that happens. But it is certainly a possibility."
The flurry of tweets on Sunday came as Trump approaches the end of his Asia trip. He will depart midday for Manila, the Philippine capital, for a summit meeting of Southeast Asian leaders.
"Will be doing a joint press conference in Hanoi, Vietnam then heading for final destination of trip, the Phillipines," Trump wrote, misspelling the name of his next stop.
Trump had remained dutifully on script during his visits to Japan, South Korea, China and Vietnam, including on Twitter, where his postings have stuck to the talking points he's delivered during his stops.
But after a formal meeting with Putin was stymied during his visit to an economic summit in Da Nang, Vietnam, Trump held forth with reporters about the damage the Russia investigations unfolding in Washington
are having on Washington-Moscow ties.