Potentially complicating matters, Trump posted a message Friday on Twitter, dismissing the Russia-related probe as a "witch hunt" and lamenting that he's "being investigated for firing the FBI Director by the man who told me to fire the FBI Director!"
The New York Times sued the FBI on Friday, seeking a court's help in getting the agency to turn over documents created by fired FBI Director James Comey after his conversations with President Donald Trump.
In another tweet posted about two hours earlier on Friday morning, Trump, for the second consecutive day, went directly after DOJ's Russian Federation probe, which now includes an examination of whether the president obstructed justice when asking Comey to drop a probe of his first national security adviser, Michael Flynn, or by firing Comey.
"The way the director handled the conclusion of the email investigation was wrong", Rosenstein wrote, failing to acknowledge the fact Trump cheered Comey's inquiry of Clinton on during the 2016 campaign.
The president tweeted Friday, "Despite the phony Witch Hunt going on in America, the economic & jobs numbers are great".
The morning missive appeared to refer to Rod Rosenstein, the deputy attorney general.
The US president has denied trying to influence the investigation, but has acknowledged in an interview that Russian Federation was on his mind when he dismissed Comey. A day later, Mr Rosenstein appointed Mr Mueller, who was at the helm of the Federal Bureau of Investigation during the September 11 attacks, as special counsel.
Trump's personal lawyer, Michael Cohen, also has retained an attorney to represent him.
Comey told a Senate panel last week he believed Trump fired him because of the Federal Bureau of Investigation's Russian Federation probe. Chuck Schumer, D-N.Y., wrote his own letter, insisting that Rosenstein's hard-earned reputation as an "apolitical actor" was "now imperiled" by the deputy attorney general's role in Comey's firing. Investigators have also been looking for any evidence of possible financial crimes among Trump associates, officials said. The order also demands that records be kept on any foreign travel by members of Trump's transition team and presidential campaign.
The US leader thinks he is the victim of a conspiracy aimed at discrediting his leadership and ending his time in the White House, according to the Associated Press.
The Trump tweets come after the top lawyer for his transition team warned organization officials to preserve all records and other materials related to the Russian Federation probe. Trump fired Comey on May 9.
Mr Trump, who is due to give a speech in Miami on Friday where he is expected to announce a shift in USA policy towards Cuba, also boasted about his deployment of social media, despite warnings by legal experts that his tweets may be used against him in the ongoing investigation.