The speaker went on to say Russian Federation has meddled in other country's elections.
Some lawmakers said they would seek remedies against Russian Federation in Congress.
Condemnation was swift, unrelenting and bipartisan.
Moments earlier, Senate Republican leader Mitch McConnell issued a public reassurance to USA allies in North Atlantic Treaty Organisation and Europe with whom Trump clashed during his frenzied Europe trip last week.
Trump claimed to have not understood what all the negative response was about.
"I mean, that is so offensive, and so insane", he said. "What's the big deal?" But apologies and clarifying statements just aren't Trump's style.
"What's more trivializing than equating a press conference between two foreign leaders - even if you think Trump didn't handle himself well - with the start of the Nazis extinguishing of Jews on a genocidal scale?" he said. "This answer by President Trump will be seen by Russian Federation as a sign of weakness and create far more problems than it solves", Graham tweeted.Republican US senator John McCain accused Trump of failing to defend his country, calling his meeting with Putin a "tragic mistake".
Or he is so profoundly ignorant, insecure, and narcissistic that he did not realize that, at every step, he was advancing the line that Putin hoped he would advance, and the line that the American intelligence, defense, and law-enforcement agencies most dreaded.
Congressman Lamborn has not made any statements regarding the Trump-Putin meeting.
As I've said in the past - President Trump should never take Putin's word at face value and should give greater consideration to U.S. Intelligence agencies over the Kremlin's rhetoric.
He also said special counsel Robert Mueller should be allowed to finish his investigation. Yet in a sign that he cannot fully accept those findings - seeing them as a challenge to his legitimacy - he added that it "could be other people also". Could be other people also.
Second, consider Trump's comments in their original context.
On Tuesday, Trump said he misspoke and instead meant to say he didn't see any reason why it wouldn't be Russian Federation. I've seen no evidence of that.
"My people came to me, [Director of National Intelligence] Dan Coats came to me and some others, they said they think it's Russian Federation". They're missing. Where are they? 33,000 emails gone, just gone. "And I think we're all to blame". Here's the deal with Clinton's emails.
Trump, whose summit with Putin concluded a week-long Europe trip that included a North Atlantic Treaty Organisation meeting and talks with British Prime Minister Theresa May, pushed back on Tuesday at the storm of criticism, blaming media coverage.
Texas Sen. John Cornyn, another Trump supporter, said, "I don't know what the president's mental calculation was in giving Putin a pass". The third is that he is acting this way toward Russian Federation because of some financial desire, like building a Trump Tower in Moscow.
While the headline on the front of Russia's MK newspaper read: "Trump and Putin exchanged being late".
For many Republicans, the issue goes beyond politics.
Trump's reference to his North Atlantic Treaty Organisation performance carried an edge, too, since the barrage of criticism and insults he delivered there was not generally well-received.
Trump's Europe trip "revealed that the president is now unbound, acting in accordance with his visceral beliefs about America's role in the world", said Thomas Wright, director of the Center on the United States and Europe at the Brookings Institution. Trump just explained away the most obvious way in which he undercut the intelligence community's assessment.
Republican Senator Jeff Flake, a longtime Trump critic, has raised the idea of passing a resolution that would voice lawmakers' support for the USA intelligence community and US allies, many of who are feeling the sting of strong Trump criticism in recent weeks.
The problem for Trump is that it will be hard for him to clean up his comments further.
'You stood there like a little wet noodle, like a little fan boy.