An animated version online shows President Trump fully transforming into Putin in about 15 seconds.
The issue has hogged national attention in the last few days after Putin made a suggestion on this lines in the context of Russia helping in the ongoing USA investigation of alleged Russian interference in the 2016 presidential polls.
The White House continued to fuel the week-long fire when White House press secretary Sarah Huckabee announced on Wednesday that Trump was considering a widely-panned request from Russian Federation.
There was no immediate reaction from the Kremlin to the invitation, but ambassador Anatoly Antonov said Moscow "was always open to such proposals".
The news comes as the United States director of national intelligence Dan Coats revealed that he does not know what was said between the two leaders during their one-on-one meeting.
After taking a deep breath he continued, "OK".
He laughed and said: "That's going to be special".
Back at home, however, Trump has come under a downpour of criticism for the ostensibly insufficiently tough position on the much-rumored "Russian meddling" in the USA presidential race in 2016.
The Senate effectively rebuked Trump for considering Putin's request to question USA officials, including President Barack Obama's former US ambassador to Moscow, amid rising concern in Washington that the rest of the US government still doesn't know what happened in Trump and Putin's private meeting in Helsinki on Monday.
Coats, who is charged with overseeing 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.
In a rebuke to the president, the Senate - controlled by Trump's fellow Republicans - unanimously approved a resolution expressing congressional opposition to any USA officials being questioned with Russian officials.
Sen. Marco Rubio, a Republican from Florida, has worked alongside Maryland Democratic Sen.
On Thursday, Sanders said in a statement that Trump disagreed with the proposal. On Tuesday, Trump said he had misspoken when he said he did not see a reason why it would have been Russian Federation that meddled, and had actually meant to make the opposite statement.
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As for Putin's offer on investigations, Sanders it was "made in sincerity" and the U.S. hopes he will have the indicted Russians "come to the United States to prove their innocence or guilt".
Russian politicians also criticized proposals by US lawmakers to question Trump's interpreter from the Helsinki summit about what topics the men discussed privately.
Earlier in the administration, Coats' voice was drowned out by the more outspoken Mike Pompeo, who was Central Intelligence Agency director before Trump tapped him as secretary of state.
He said he looked forward to a second meeting with Putin to tackle the issues.
The Senate, though, made their stance on the suggestion official with a resolution introduced by Sens.
But, Coats added, Trump was right to point out this week that Russian interference is just one of many potential threats facing the country. "That's not going to happen", US Secretary of State Mike Pompeo told CBN News on Thursday.
"Obama didn't do it", Trump told CNBC in an interview at the White House. But U.S. Defence Secretary Jim Mattis has given no public indication since the summit of plans to work more closely with the Russian military in Syria. "Many positive things will come out of that meeting".
KIM: He's happy, but I think he's also quite cautious.
He last visited the White House in 2005, when he met President George W. Bush, who welcomed the Russian leader in the East Room as "my friend". It took the president several attempts to walk back his comments, amplifying the fallout from his joint appearance with Putin.
While the White House appeared to be considering the idea, lawmakers scrambled to issue a unified response against Russian Federation.
Sen. Jeff Flake, R-Ariz., said it's what happens "when you wage war on objective reality for almost two solid years, calling real things fake and fake things real".
"We will see how things develop further, ' Mr Putin said, evoking unnamed "forces" in the U.S. trying to prevent any improvement in relations and 'putting narrow party interests above the national interest".
Both Trump and Putin earlier on Thursday praised their first meeting as a success and blamed forces in the United States for trying to belittle its achievements.