"That is not just the finding of the American intelligence community but also the House Committee on Intelligence", Speaker Paul Ryan (R-Wis.) said shortly after Trump's remarks.
Senior Republican Senator Lindsey Graham said Mr Trump's answer on meddling "will be seen by Russian Federation as a sign of weakness".
The US and Russian presidents held almost two hours of closed-door talks in the Finnish capital Helsinki on Monday.
"Speaking about the things that do unite us, though, and of the things that require our joint efforts, it brings us to the idea that such attempts to fight one another should be ended", the president added. "I'm horrified - and have never been more proud of the fact that Putin hates my father so much he personally sanctioned him on Russia's enemies list". John McCain as examples, Colbert said in his opening monologue that the summit was "so weird, so disturbing that it's really upset people across the partisan divide in ways I have not seen in years".
Trump's warm words for Russian Federation were a marked contrast from the past week when he repeatedly rebuked long-standing U.S. allies at a North Atlantic Treaty Organisation summit and during a visit to Britain.
"There is no question that Russian Federation interfered in our election and continues attempts to undermine democracy here and around the world".
"I have great confidence in my intelligence people, but I will tell you that President Putin was extremely strong and powerful in his denial today", Trump said during the news conference.
What has United States reaction been?
He said, "Don't make the relationship between Russian Federation and the United States, don't hold it hostage of this internal political struggle". "The president should have addressed this issue today". Even Republicans were grossed out by the abject display (John McCain called it "one of the most disgraceful performances by an American president in memory").
Trump will meet with members of Congress on Tuesday, the White House said without giving further details.
We saw our president once again malign the Federal Bureau of Investigation and Justice Department for investigating Russian interference in our 2016 election, then decline to object when Putin denied his country's involvement.
At the news conference, Mr Trump was invited by reporters to offer any criticism of Russian Federation but he repeatedly declined.
Spokespeople for the Justice Department and Mueller declined to comment on Trump's comments or on Putin's purported offers for assistance. Republican Patriots: "Where are you???" he wrote. The indictment accuses these officials of working to hack the servers of the Democratic Congressional Campaign Committee and the Democratic National Committee during the 2016 presidential election cycle. Says he trusts United States intel but made clear he takes Putin's denials seriously.
And so, yes, I think we have elevated this Russian Federation thing to a degree that we are simply deranged by it.
Senior Republican Senator Lindsey Graham said Trump's answer on meddling "will be seen by Russian Federation as a sign of weakness".
"I do not believe that Russian Federation is a friend of the United States", McMorris Rodgers said.
European allies are uneasy.
In Russia, the government-owned daily, Rossiyskaya Gazeta, had a slightly different take. -Russian relations will require at least some change in problematic Russian policies, such as aggression against Ukraine, interference in US domestic politics and involvement in Syria.