Meanwhile, Vice President Mike Pence's office confirmed yesterday that he has retained Richard Cullen, a former USA attorney and the former Virginia attorney general, in response to the investigation.
"After 7 months of investigations & committee hearings about my "collusion with the Russians", nobody has been able to show any proof".
Rosenstein in a memo to Trump raised concerns over FBI Director James Comey.
Meanwhile, special counsel Robert Mueller - a respected former Federal Bureau of Investigation director - has sought to beef up his investigatory firepower. The Washington Post reported this week that Mueller is investigating whether Trump attempted to obstruct justice when he suggested Comey drop an FBI investigation into Michael Flynn, Trump's former national security adviser, as well as when he fired Comey.
But Rosenstein is not now heading the FBI's probe into the Trump campaign's possible collusion with a Russian campaign that USA intelligence officials have said was seeking to tilt the outcome of the 2016 election in Trump's favor.
The president made a tweet about his defeated Democratic opponent complaining that the probe is unfair.
"Why is that Hillary Clintons family and Dems dealings with Russian Federation are not looked at, but my non-dealings are?" the president tweeted.
Obstruction of justice is an impeachable offense. "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.
"You are witnessing the single greatest WITCH HUNT in American political history - led by some very bad and conflicted people!" he said in an early morning tweet.
Trump has repeatedly sworn that he is personally not under investigation, and Comey assured him that he wasn't.
Pence retained Richard Cullen, a partner at McGuire Woods in Richmond, Virginia, who previously served as a US attorney for the Eastern District of Virginia and has extensive experience with government investigations.
Mr. Mueller's investigation appeared to be reaching a circle of current and former officials. The US president is reportedly probed over obstruction of justice. Comey, after all, could only testify that Trump wasn't a target of the probe as of early May, when he was sacked.
He reiterated tweets from Thursday morning about the investigation. Though some in the White House have preached caution, fearing a repeat of the firestorm over Comey's firing, many in Trump's orbit - including his son Donald Trump Jr. and adviser Newt Gingrich - have deemed Mueller biased and worthy of dismissal.