Previously, Trump was forced to walk back his Helsinki statements, where he was asked about the Kremlin's alleged interference and replied by saying that Putin "just said it's not Russian Federation".
"I think it's imperative that he understand that he's misjudging Putin", Graham told reporters.
That offer was to allow the U.S. to question 12 Russians accused of interfering in the 2016 presidential election, in exchange for Russia being allowed to interview Americans they had accused of unspecified crimes.
It was the first clarification that had to be issued after a number of deeply controversial comments made by Mr Trump during that news conference.
"Here's what I said about Putin's Russia", Clinton tweeted.
"The sentence should have been: "I don't see any reason why I wouldn't" or 'why it wouldn't be Russian Federation", he told reporters at the White House.
"Gingrich added that the Trump administration is now getting into its next phase of foreign policy, including with China, North Korea and Russian Federation, and he predicts the American side will be 'remarkably tough".
"As I expressed to the president on my third visit to the Oval Office as his adviser, I said: 'Mr".
Earlier Mr Trump rejected a proposal by Mr Putin that Russian Federation be allowed to question U.S. citizens.
The zigzagging laid bare the White House's search for a path out of trouble that has dogged the administration's discussions of Russian Federation from the start, but spiraled after Trump's trip to Helsinki.
Putin offered to allow investigators involved in the special counsel Robert Mueller's probe to interview 12 Russian intelligence officers who were recently indicted in exchange for Russian access to Browder and other USA officials.
Trump has weathered heavy criticism from Democrats and Republicans alike for his performance at the meeting, where he publicly sided with Putin over United States intelligence agencies' assessment that the Russians interfered in the 2016 presidential election.
What else has happened since the Trump-Putin summit?"President Putin was extremely strong and powerful in his denial today".
The offer Putin described was to permit American law enforcement officials to observe questioning by Russian officials of the indicted Russians in exchange for letting Russian investigators question Americans on other matters, specifically mentioning a case involving London-based financier Bill Browder, a onetime investor in Russia.
At a post-summit news conference with Putin, Trump responded to a question about Russian meddling in the 2016 US presidential election by casting doubt on the findings of his own intelligence agencies and denouncing the "stupidity" of USA policies.
But he said he believed that "Russia's actions had no impact at all on the outcome of the election".
Sanders called the legislation "hypothetical" and declined to say whether the president would back it. John McCain, R-Ariz., or Richard Shelby, R-Ala., voting. A similar House vote Tuesday failed on a party-line vote. "Well, you're right, I don't know what happened at that meeting", Coats said in response to a question at the Aspen Security Forum in Colorado.