Mr Trump tweeted: "I am being investigated for firing the FBI Director by the man who told me to fire the FBI Director!"
Earlier this month, Rosenstein told The Associated Press that "if anything that I did winds up being relevant to his investigation then, as Director Mueller and I discussed, if there's a need from me to recuse, I will". And a person familiar with Trump's thinking said Tuesday morning that it's "unlikely" the President will fire Mueller, but conceded that it's often hard to predict Trump's behavior. Recent news reports have suggested Trump sought all three officials' help in pressuring FBI Director James Comey to drop his investigation into former National Security Adviser Mike Flynn.
The complaints Trump aired Thursday afternoon followed a pair of morning tweets.
The White House confirmed Thursday that Mueller was interviewed, presumably about again running the Federal Bureau of Investigation, the day before he was named as special counsel to investigate Russian meddling in last year's presidential election.
The White House has said the subsequent meeting with the banker was a pre-inauguration diplomatic encounter, unrelated to business matters.
Rosenstein wrote a memo recommending May 9 Comey's firing.
Starr's op-ed follows comments he made on CNN's "New Day" Thursday morning in which he said there is now no obstruction of justice case against Trump, based on the evidence that has been made public so far.
AG Sessions to testify in public Tuesday
Rosenstein will take his place before both the House and Senate subcommittees to testify about the Justice Department's budget. Those reports led Sessions to recuse himself from the investigation into alleged Russian meddling in the presidential contest.
Trump ignored shouted questions from reporters about the ongoing Russian Federation controversy as he departed the White House Friday for Miami.
Although he was brought on to lead the Russian Federation investigation, Mueller is allowed to look beyond it.
Deputy Attorney General Rod Rosenstein issued a statement on Thursday urging Americans to "exercise caution before accepting as true any stories attributed to anonymous 'officials, ' particularly when they do not identify the country - let alone the branch or agency of government - with which the alleged sources supposedly are affiliated".
It wasn't clear whether the president was basing his tweet on direct knowledge that he is under investigation, or on reports this week that special counsel Robert Mueller is examining whether the president obstructed justice by firing Comey last month amid the ongoing Russian Federation investigation. Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, in a statement. "President Trump said prior that once he gets in he's going to kick the S-H-I-T out of the enemy". "That's undemocratic on its face and a blatant violation of the president's oath of office". Trump conceded in an interview after the episode that he was thinking about the Russian Federation controversy when he made that decision. Some of his ire is aimed at Rosenstein and investigative special counsel Robert Mueller, both of whom the president believes are biased against him, associates say. But Rosenstein, too, may ultimately have to hand off oversight given his role in Trump's decision to fire Comey.
Comey stated during questioning by Senator Marco Rubio that Trump did not direct the then FBI director to stop the investigation of former National Security Adviser Michael Flynn ties with Russian Federation, but expressed a wish for the matter to end.
Trump and his supporters have repeatedly complained about leaked reports on the progress of Mueller's investigation, many of which have appeared in either the Post or The New York Times.