When asked why not release details of the almost two-hour conversation, Trump said: "I would, I don't with care".
The Times reported that FBI agents and some top officials became suspicious of Trump's ties to Russian Federation during the 2016 presidential campaign but didn't launch an investigation at that time because they weren't sure how to approach such a sensitive and important probe, according to the unnamed officials.
Trump dismissed the notion in Saturday's interview, but without ever directly denying that he was working as a secret agent for Russian Federation.
Robert Mueller has spent 20 months investigating Russian interference in the 2016 United States presidential election, and possible collusion between the Trump's campaign and Moscow.
He slammed the Times story as "the most insulting article I've ever had written and if you read the article, you'd see that they found absolutely nothing".
Trump made the demand after a July 2017 meeting with the Russian president at the G-20 conclave in Hamburg, Germany, which was also attended by then-Secretary of State Rex Tillerson, the paper reported Saturday.
Trump's secrecy surrounding Putin "is not only unusual by historical standards, it is outrageous", said Strobe Talbott, a former deputy secretary of state now at the Brookings Institution, who participated in more than a dozen meetings between former presidents Bill Clinton and Boris Yeltsin in the 1990s.
The Post's report comes less than 24 hours after a bombshell New York Times report that revealed President Trump has been the target of a counterintelligence investigation by the FBI, which began nearly immediately after he fired Jim Comey.
"I mean, it's so ridiculous, these people making up", Trump said, claiming the Post is a "lobbyist" for Bezos' interests.
Chelsea Turn Down Willian Malcom Swap Deal Approach from Barcelona
England winger Jadon Sancho will reject advances from the Premier League and has insisted he wants to stay at Borussia Dortmund. Moreover, Chelsea have recently signed Christian Pulisic, who will probably further reduce the game time of Willian .
"The president also again defended his firing of ex-FBI Director James Comey, voicing outrage over a New York Times report that as a result of the firing, the FBI had investigated if Trump was secretly working on behalf of Russian Federation".
Robert Mueller took over the investigation when he was appointed special counsel soon after Comey's firing.
"Over time it got harder and harder, I think, because of a sense from Trump himself that the leaks of the call transcripts were harmful to him", said a former administration official.
Following the Hamburg meeting, the U.S. leader took away the notes of his interpreter and instructed the person to keep quiet on what was said, the paper reported.
Trump tweeted early on Saturday that the report showed that the FBI leadership "opened up an investigation on me, for no reason & with no proof" after he had fired Comey.
Trump disclosed classified information about a terror plot, called former Federal Bureau of Investigation director James Comey a "nut job", and said that firing Comey had removed "great pressure" on his relationship with Russian Federation.
Trump's ex-national security adviser, Michael Flynn, pleaded guilty to lying to investigators about his Moscow ties.
And Trump's former presidential campaign chairman, Paul Manafort, has been convicted in one case brought by Mueller and pleaded guilty in another, over financial crimes related to his work in Ukraine before the 2016 campaign, and for witness tampering.
"Cohen, who will testify in Congress on February 7, insists that he has never been to Prague, but added in a tweet: "#Mueller knows everything!"