Mr Rosenstein played a part in the dismissal of former Federal Bureau of Investigation director James Comey who was sacked by Mr Trump in May.
Donald Trump has reportedly been yelling at TV sets in the White House as he becomes "increasingly angry" about an investigation into alleged Russian meddling in the United States presidential election. The revelation led many to believe Trump was planning on firing Rosenstein from the Justice Department, or that the deputy attorney general had possibly refused to fire Mueller on Trump's behalf. Rosenstein in a memo to Trump raised concerns over Comey, and later appointed Mueller as special counsel.
The White House confirmed Mr Mueller was among the candidates the president interviewed to replace Mr Comey.
During congressional testimony, Comey described the allegations as "lies, plain and simple".
Trump admitted in an interview with NBC News' Lester Holt days after Comey's ousting on May 9 that the Russian Federation investigation influenced his decision to terminate him.
Citing Rosenstein's private remarks, ABC News reported that he may have to recuse himself from the investigation, potentially following in the footsteps of Attorney General Jeff Sessions who did so in early March in a move that continues to vex the American president.
Press Secretary Sean Spicer recently confirmed President Trump's tweets are in fact official statements. "With all of the illegal acts that took place in the Clinton campaign and the Obama administration, there was never a special counsel appointed", Trump had tweeted. Those associates include former national security adviser Michael Flynn, campaign chairman Paul Manafort, foreign policy aide Carter Page and outside adviser Roger Stone.
Former FBI Director James Comey testifies before a Senate Intelligence Committee hearing on "Russian Federation Efforts to Interfere in the 2016 U.S. Elections" on Capitol Hill in Washington, U.S. June 8, 2017.
"He's driving this", the White House official said, speaking on condition of anonymity to discuss West Wing internal deliberations.
Although he didn't name anyone, Trump appeared to be pointing the finger at Rod Rosenstein, the deputy attorney general who began overseeing the Russian Federation investigation after Attorney General Jeff Sessions recused himself from it.
The order came the same day that Vice President Mike Pence hired an outside lawyer to represent his legal interests.
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