Mueller will have broad powers in his new role and the latitude to investigate anything related to the Trump campaign's ties to Russian Federation and potential collusion with Russian Federation to interfere in the 2016 election.
Separately, the New York Times (NYT) reported that Mr Trump had told Russian officials at a recent White House meeting that firing Mr James Comey as Federal Bureau of Investigation director relieved "great pressure" on him.
The White House did not deny that Trump had been critical of Comey to Russian officials.
Meanwhile, the Senate's investigation of the Trump campaign's ties to Russian Federation appears to be accelerating, with Comey on Friday agreeing to testify before the panel.
The naming of Mueller as special counsel comes a week after Trump abruptly fired James Comey, the man who succeeded him as FBI Director.
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Late on Friday, the Senate intelligence committee announced that Mr Comey had agreed to testify at an open hearing at an undetermined date after Memorial Day.
The White House initially attributed the firing to Comey's handling of the investigation into Hillary Clinton's email server, while Democrats and the press suspected an effort to disrupt the FBI's Russian Federation investigation. The director had some hope that, over time, he could effectively point out the appropriate procedures and guidelines to both Trump and the White House staff about how the process of communications normally works.
The day after firing Mr Comey, Mr Trump hosted Russian Foreign Minister Sergei Lavrov in the Oval Office, along with Mr Kislyak.
Senator Mark Warner, the committee's vice-chairman, said Comey "deserves an opportunity to tell his story". "Moreover, the American people deserve an opportunity to hear it".
But it lead to criticism from Mr Trump's political rivals, including Democratic Leader Nancy Pelosi, who said earlier this week: "If these reports are true, the President's brazen attempt to shut down the FBI's investigation of Michael Flynn is an assault on the rule of law that is fundamental to our democracy".
Former FBI Director James Comey Will Testify In Open Session
Trump declared himself the victim of the "greatest witch hunt" in American political history and denied allegations of collusion. The White House has struggled to explain the chain of events that led to Mr Comey's firing and exactly who made the decision.
However, Comey declined an invitation from the Senate judiciary committee to testify about the circumstances of his firing and interactions with officials from the Trump and Obama administrations related to the Russian Federation and Hillary Clinton investigations. "He and I have an unwritten secret agreement that I don't talk about his job", Comey senior said.
And according to a report from Reuters, the White House is already trying to use this statute to undermine Mueller's credibility.
Wittes, a friend of Comey, described him as being disgusted by Trump's efforts to gain his loyalty and establish a personal relationship, which Comey considered inappropriate.
The ex-FBI chief has not spoken publicly since his surprise firing last week.
Comey Agrees to Testify in Open Hearing Before Senate Intel Committee
Mr Comey is known to produce memos documenting especially sensitive or unsettling encounters, such as after the February meeting. Diane Feinstein (D-CA), expressing their "extreme disappointment" at Comey's apparent refusal to testify before their committee.