President Trump on Friday tweeted that despite the months of investigations and hearings, no proof had emerged.
He said: "I am being investigated for firing the FBI Director by the man who told me to fire the FBI Director!" "Witch Hunt", the President tweeted.
In a survey of registered voters, 45 percent said they trust Comey to tell the truth, while 32 percent said they trust Trump.
At a ceremony last month to welcome Associate Attorney General Rachel Brand, the Justice Department's third-ranking official, Rosenstein joked awkwardly about being at the center of criticism since taking office, according to people who were in the room.
Robert Mueller, the special counsel probing Russia's interference in the 2016 USA presidential elections and its possible collusion with figures in the Donald Trump campaign, is reportedly investigating the financial dealings of the president's senior adviser and son-in-law, Jared Kushner.
The Post report cited anonymous sources who were briefed on requests made by investigators.
The Post reported that the obstruction of justice investigation of the president began days after James Comey was sacked as the FBI Director on May 9.
Mueller is in the preliminary stages of his probe and has recruited a team of top investigators experienced in money laundering, campaign finance violations and eastern European organized crime.
Moment of silence for London fire victims
Hundreds have been left homeless by the blaze, putting more pressure on officials in a city plagued by a chronic housing shortage. May said after the meeting Saturday that there have been "huge frustrations" in the community as people tried to get information.
Mr Mueller is leading an Federal Bureau of Investigation inquiry into Russia's alleged meddling in the 2016 presidential election. Joe Lieberman, former Oklahoma Governor Frank Keating, former FBI official Richard McFeely and acting FBI Director Andrew McCabe, met with Trump at the White House.
In an interview with NBC's Lester Holt on May 11, Trump said he was "going to fire [Comey] regardless of recommendation" from Rosenstein and Sessions.
He was answering accounts that he is personally being investigated for obstruction of justice with a characteristic scorched-earth defence: claiming mistreatment of historic proportions and calling into question the probity of his accusers.
Mark Corallo, a spokesman for Trump's personal lawyer, responded Wednesday evening to the Post report by saying: "The FBI leak of information regarding the president is outrageous, inexcusable and illegal".
Trump also took aim at his favorite foil - the media.
If that is the case, it could be part of what appears to be a pattern of statements that are meant to back the president.
"We do not know what this report refers to", attorney Jamie Gorelick said in a statement. "I hope you can let this go". "That was his promise and that's exactly what we're doing".
President Donald Trump on Friday confirmed he was under investigation in an ongoing probe about Russian interference in the election, and he appeared to attack the man in his administration overseeing it.
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