Additionally, he took the opportunity to highlight some perceived presidential wins, while continuing to decry the "phony Witch Hunt".
Deputy Attorney General Rod Rosenstein, who appointed Mueller last month, testified Tuesday he has seen no evidence of good cause to fire Mueller. Earlier, Rosenstein had authored an extensive and publicly-released memorandum recommending former FBI-chief James Comey's firing.
"But let me be very clear here, as it has been since the beginning, the president is not and has not been under investigation for obstruction", he added. Rosenstein, who would be responsible for actually dismissing Mueller, told USA lawmakers he would fire him only with good cause. In one, he told CBS's Face the Nation that "there has been no notification from the special counsel's office that the president is under investigation".
Aides have counseled the president to stay off Twitter and focus on other aspects of his job. The White House denies any collusion.
Mueller reports to Rosenstein on budget and staffing needs for his team.
Trump's lawyer also took aim at Mueller on Sunday, claiming the President is not being investigated by Mueller, despite Trump tweeting otherwise on Friday.
Trump may have attempted to obstruct justice when he reportedly urged former FBI Director James Comey to throw out any investigation into Trump's former national security adviser Michael Flynn. Rosenstein issued a statement expressing confidence in Mueller.
In the statement Thursday evening, Rosenstein warned that USA citizens should be skeptical about anonymous allegations. Among other roles, she was an official in the Justice Department's Office of Legal Policy under George W. Bush. Trump has repeatedly complained about the probe, saying Democrats can not accept his election win. An official of Trump's transition confirmed the laywer's internal order sent Thursday.
The story was attributed to "U.S. officials familiar with the matter".
The day after Comey's firing on May 9, he told reporters on the Hill, "He is a man of extraordinary independence and integrity and a reputation in both political parties of great character".
Obviously, it is to be hoped Mueller will conduct a thorough, impartial probe.
Donald Trump smiles during a meeting with cabinet members at the White House on Monday.
He cited the recommendation of Attorney General Jeff Sessions, who has recused himself from the Russian Federation inquiry, and his deputy Rosenstein.
Court justice nominated by President Trump. But it was Rosenstein who later appointed Robert Mueller as a special counsel to oversee the investigation into Russia's election meddling and any possible ties to the Trump campaign. He then stated again that Trump was not being investigated.
If Rosenstein recuses himself from oversight of the special counsel investigation, that role would fall to the Justice Department's No. 3 official, newly confirmed Associate Attorney General Rachel Brand.
White House spokesman Mark Corallo said: "The FBI leak of information regarding the President is outrageous, inexcusable and illegal".
Trump, who hired his own lawyer last month regarding the probe, kept up his criticism of the investigation.