Rosenstein was also the author of a memo recommending the dismissal of FBI Director James Comey, which the White House cited along with a memo from Sessions as the reason Trump fired Comey on May 9.
"A special counsel investigating the president of the United States must first and foremost be beyond the question of conflict", he said. A day later, Rosenstein appointed Mueller, who was at the helm of the Federal Bureau of Investigation during the September 11 attacks, as special counsel.
California Sen. Dianne Feinstein said she is concerned that Trump might try to fire both Rosenstein and Mueller. Rosenstein, who would be responsible for actually dismissing Mueller, told US lawmakers he would fire him only with good cause.
Aides have counseled the president to stay off Twitter and focus on other aspects of his job.
By having Mueller on board for the Russian probe, Rod J.
Robert Mueller, the special counsel named by the department to investigate the Russian Federation matter, is now examining whether Trump or others sought to obstruct the probe, a person familiar with the inquiry said on Thursday.
Yet Trump's angry tweets on Friday underscored the near-impossible challenge his advisers and legal team have in trying to get him to avoid weighing in on an active probe. Mueller was appointed under a rarely used regulation that gives him a broad mandate to investigate just about anything he feels is necessary, which could ultimately include Rosenstein's role in Comey's firing. Americans should be skeptical about anonymous allegations. Trump has repeatedly complained about the probe, saying Democrats can not accept his election win.
If Rosenstein recuses himself, Brand, a Trump appointee, would become the top Justice official overseeing Mueller's work.
The transition official spoke on condition of anonymity because the person was not authorized to discuss post-election decisions publicly. Comey's firing likely will be part of that probe. "Absent the most extreme circumstances, the President would be singularly ill-advised to threaten, much less order, Mueller's firing".
Ruddy, who had been at the White House on Monday, told PBS that Trump is considering terminating the special counsel. It added that the president was not personally notified that he would be probed for obstruction of justice.
FILE - In this June 13, 2013 file photo, then-FBI Director Robert Mueller testifies on Capitol Hill in Washington.
Mr Mueller was appointed as special counsel to investigate Moscow's involvement in the presidential election previous year and possible collusion by Trump campaign associates with the Russians, but there has been no indication that Mr Mueller told the president to fire Mr Comey.
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.
Trump seemed to confirm that story - his White House hadn't denied it but instead condemned the leak from which it sprang - in a Friday morning tweet.
The memos direct former staffers to prevent the automatic deletion of any records and former Trump transition officials are asked to send in materials to the Trump transition team.
Vice President Mike Pence has hired his own lawyer to represent him in the special counsel investigation and congressional inquiries into Russia's role in the 2016 election.
"Failure to follow these protocols could result in criminal or civil penalties, and could form the basis of legal claims, legal presumptions, or jury instructions relating to spoliation of evidence", the memo warns former Trump transition team members.