After face-to-face talks with Russian President Vladimir Putin, Mr Trump contradicted US intelligence agencies and said there had been no reason for Russia to meddle in the vote.
Mr Putin reiterated that Russia had never interfered in US affairs.
The two men held nearly two hours of closed-door talks in the Finnish capital Helsinki on Monday.
At a news conference after the summit, President Trump was asked if he believed his own intelligence agencies or the Russian president when it came to the allegations of meddling in the elections.
“President Putin says it’s not Russia. I don’t see any reason why it would be,” he replied.
US intelligence agencies concluded in 2016 that Russia was behind an effort to tip the scale of the US election against Hillary Clinton, with a state-authorised campaign of cyber attacks and fake news stories planted on social media.
What has US reaction been?
In a strongly-worded statement, US House Speaker Paul Ryan said Mr Trump “must appreciate that Russia is not our ally”.
“There is no moral equivalence between the United States and Russia, which remains hostile to our most basic values and ideals,” he said, adding that there was “no question” Moscow had interfered in the 2016 election.
Senior Republican Senator John McCain said it was a “disgraceful performance” by a US president.
“No prior president has ever abased himself more abjectly before a tyrant,” Mr McCain said in a statement.
Another senior Republican, Senator Lindsey Graham, who is a member of the Senate Armed Services Committee, tweeted that it was a “missed opportunity… to firmly hold Russia accountable for 2016 meddling”.
In a series of tweets, Senate Democratic leader Chuck Schumer said Mr Trump’s actions had “strengthened our adversaries while weakening our defences and those of our allies”.
The US Director of National Intelligence, Dan Coats, also issued a statement saying that the intelligence community had been clear about Russia’s “ongoing, pervasive attempts” to undermine US democracy.
Mr Trump responded by tweeting that he had “great confidence in my intelligence people”, adding: “I also recognise that in order to build a brighter future, we cannot exclusively focus on the past – as the world’s two largest nuclear powers, we must get along.”
Vice-President Mike Pence, in a speech at the US Department of Commerce, defended the summit and praised President Trump.
Speaking on Monday, President Putin offered to allow US investigators to visit Russia to question the officers.
He made it clear that, in return, Russia would want similar access to people in the US it suspects of criminal activity.
Trump targets opponents back home
Analysis by Jonathan Marcus, BBC diplomatic correspondent
Before their encounter started, Mr Putin was already winning on points, by the mere fact that President Trump was meeting him in the first place.
But while Mr Putin came over as the seasoned professional, eager to present his country as an equivalent to the US in terms of being a nuclear superpower; an energy provider; and a key actor in the Middle East, Mr Trump seemed more intent on castigating his opponents back home.
A lot of the questions focused on Russia’s intrusion into the US election campaign (the considered position of the key US intelligence agencies) and specifically the indictment by the Mueller probe of 12 Russian intelligence agents.
Mr Trump would have none of it. He visibly seemed happier with Mr Putin’s assurances than he did with the evidence of his own intelligence agencies. And he even welcomed Mr Putin’s suggestion that Russia could join the investigation and interview the alleged perpetrators itself! Washington’s Nato allies and many seasoned observers on Capitol Hill must have been watching in horror.
Mr Putin described the Helsinki meeting as “candid and useful” while Mr Trump said there had been “deeply productive dialogue”.
Mr Trump said US-Russia relations had “never been worse” than before they met, but that had now changed.
Relations between Russia and the West were severely strained by Moscow’s annexation of Crimea in 2014, which President Putin acknowledged in the news conference.
“President Trump’s position on Crimea is well known. He talks about the illegality of the Crimean reintegration to Russia. We have another point of view… that a referendum was held in accordance with international law. For us, it’s a closed question,” he said.
Both leaders also said they would work together to help resolve the Syrian crisis. The US and Russia back opposing sides in the eight-year-old civil war.
Photo Credit: WVIK