Trump's remarks followed a morning tweet in which he blamed the media for negative coverage of yesterday's news conference and said that his meeting with Putin had gone "even better" than a meeting with Nato allies the week before.
"While I had a great meeting with Nato, raising vast amounts of money, I had an even better meeting with Vladimir Putin of Russia," Trump wrote, referring to his efforts to increase defence spending by US allies. "Sadly, it is not being reported that way - the Fake News is going Crazy!"
During a remarkable 46-minute joint news conference at the end of yesterday's summit in Helsinki, Trump would not challenge Putin's claim that his Government played no role in trying to sabotage the US election in 2016, despite the indictment last week of 12 Russian intelligence officers, stemming from special counsel Robert Mueller's investigation of election meddling.
Trump's performance prompted a wave of condemnation, including from many in his own party. Today, a growing number of Republicans called for him to take swift action to embrace the US intelligence community's findings about Russian interference and limit the damage from Helsinki.
Speaking with reporters outside the Senate chamber, Senate Majority Leader Mitch McConnell did not mention Trump by name but sought to reassure allies in Europe that the United States stands with them and warned that Russian interference better not happen again.
"We believe the European Union countries are our friends and the Russians are not. They've demonstrated that in all the obvious ways over the last few years with the annexation of Crimea, the invasion of eastern Ukraine, not to mention the indisputable evidence that they tried to impact the 2016 election," McConnell said.
Pressed about Trump's remarks in Helsinki, House Speaker Paul Ryan also declined to criticise the President, focusing his response on Russia and Putin.
"Let me be really clear," Ryan told reporters at a news conference. "We stand by our Nato allies and all those countries facing Russian aggression."
The Speaker, who put out a statement yesterday supporting the conclusions of the US intelligence community, reiterated that Russia interfered in the 2016 presidential election but added that it had no material effect on the results.
Ryan, however, declined to say whether he agreed with Republicans who have called on Trump to clarify his comments.
On morning television shows and social media, several Trump supporters urged Trump to explain to the nation why he appeared to side with Putin instead of the US intelligence community, which has concluded that Russia was responsible.
"He's got to speak out about it, and he's got to reverse course immediately," former White House communications director Anthony Scaramucci said during an appearance on CNN. "The optics of this situation are a disaster. . . . If he doesn't reverse course on this, he will eventually lose people who want to support him."
Scaramucci, who said he still considers himself loyal to Trump, recommended that the President huddle with "his smartest, most loyal aides" and craft a statement making clear he understands there was Russian interference in the election.
Trump could do that while continuing to insist there was no collusion between the Russians and his campaign, Scaramucci said.
Democrats sought to capitalise on the outcry over Trump's performance.
In a speech on the Senate floor, Senate Minority Leader Charles Schumer called on the chamber's Republican leaders to schedule hearings on what occurred in Helsinki.
"Our Republican colleagues cannot just go, 'tsk-tsk-tsk,'" Schumer said. "They need to act."
Schumer said he was particularly concerned about what Trump might have said to Putin during a closed-door, two-hour meeting between the two at which only their interpreters were present.
"The American people deserve to know what's happened. Our security is at risk," Schumer said.
In a letter to colleagues, House Minority Leader Nancy Pelosi outlined several steps by the party to draw attention to Trump's meeting with Putin.
"Yesterday, President Trump cowered before President Putin, and engaged in a dangerous, disgraceful and damaging show of his Blame America First policy," she wrote.
"His total weakness in the presence of Putin proves that the Russians have something on the President, personally, financially or politically."
Pelosi said Democrats would introduce a resolution based on Ryan's statement yesterday backing the US intelligence findings and would seek to force a vote to increase funds for election security.
The Democratic National Committee sought to capitalise on the episode by sending out a fundraising solicitation asking for donations to help elect Democrats "who will hold this reckless president accountable."
Trump tweeted about the summit for the first time since his return to Washington the night before. He thanked Senator Rand Paul, (R), one of the few prominent Republicans who have defended his performance.
Earlier in the morning, Paul defended Trump on CBS, saying he has been the focus of a "partisan investigation" over Russia and is "sensitive to that."
Other Republicans weren't as forgiving.
"It was a really bad day for the President," Congressman Adam Kinzinger, (R), said on CNN. "I think President Trump was wrong yesterday in a major way, and I think it was a very embarrassing press conference."
Kinzinger said Trump needed to speak to the nation about what happened - in person and not on Twitter.
"You need to come out today and very much clarify this," he said.
Kinzinger's pleading echoed former House Speaker Newt Gingrich, a Republican who typically defends Trump.
"President Trump must clarify his statements in Helsinki on our intelligence system and Putin," Gingrich tweeted yesterday. "It is the most serious mistake of his presidency and must be corrected - immediately."
Congressman Matt Gaetz, (R), whom Trump recently endorsed for re-election, was asked during an appearance on Fox News' Fox & Friends today whether he thinks Trump should clarify his comments at the news conference.
"I look for the President to maybe illuminate a little further the progress that was made in the closed-door session," Gaetz said.
In an earlier tweet, Trump took credit for pledges from Nato allies at last week's summit in Brussels to meet their targets for defence spending - a move he said was "bad for Russia."
At a news conference following the Nato summit last week, the President claimed that alliance members had agreed to "substantially up their commitment . . . at levels that they've never thought of before." However, other Nato leaders disputed Trump's assertions, saying they had merely agreed to meet previous commitments.
While Trump characterised the North Atlantic Treaty Organisation gathering as positive, several US allies were offended by his brusque manner. At the outset of the summit, Trump claimed that a natural gas pipeline deal had left Germany "totally controlled" and "captive to Russia" as he levied fresh accusations about "delinquent" defence spending by allies.