Trump tweeted Thursday that he looked forward a "second meeting" with Putin and defended his performance at Monday's summit, in which the two leaders conferred on a range of issues including terrorism, Israeli security, nuclear proliferation and North Korea.
The invitation seemed to surprise Trump's own Director of National Intelligence Dan Coats, who was told about it during a live interview at an event in the U.S. state of Colorado.
"I think as time goes by and the President has already mentioned some things that happened in that meeting, I think we will learn more".
After the meeting, the U.S. president had declared that he believed Putin's claims that Russian Federation had not interfered in the USA presidential election.
Following the two leaders' summit in Helsinki, Finland, the White House announced it had invited Putin to visit for a second meeting in the fall, which has brought on additional criticism.
"I'll be his worst nightmare, but I don't think it'll be that way", Trump told CNBC in an interview broadcast Friday.
The criticism came after what many considered the most hard week of Donald Trump's presidency.
The shock disclosure blindsided the US President's intelligence chief Dan Coats who was speaking at a security conference when the news broke and responded with "OK".
Before the meeting in Helsinki, Coats publicly warned that the United States was facing a growing cyber threat, singling out Russian Federation as the country's most hostile adversary.
A White House spokeswoman, Lindsay Walters, wanted to make clear that the president "respects the independence of the Fed". "We are ready for discussions on that point". Standing alongside Putin, Trump called the idea "an incredible offer".
"This issue (of a referendum) was discussed", he said, adding without elaborating that Putin made "concrete proposals" to Trump on solutions for the four-year Ukraine conflict, which has killed more than 10,000 people.
Coats, who oversees the nation's 17 intelligence agencies, also said that if he had been asked, he would have advised Trump against meeting Putin alone, with just interpreters.
Graham told The Washington Post that Trump's inability to distinguish the two assertions is based on his concerns that any acknowledgement of Russia's role in the 2016 presidential election undercut his legitimacy as president.
He said: "Interference with the domestic affairs of the United States - do you really believe that someone acting from the Russian territory could have influenced the United States and influenced the choice of millions of Americans?"
The White House on Friday also said it was rejecting a proposal from Putin to hold a referendum in eastern Ukraine, calling the Russian leader's suggestion "illegitimate". Members of Congress said they want to learn more about their closed-door meeting in Helsinki and whether Trump made commitments to his Russian counterpart.More news: Survivor: Duck boat captain said life jackets not needed