The announcement by Deputy Attorney General Rod Rosenstein pleased the Democrats and other critics of Mr. Trump, who have been clamouring for a special counsel to lead the probe.
The Republican leader, who has struggled to shake off suspicions that Russian Federation helped put him in the White House, has been accused of seeking to block the investigation by firing FBI chief James Comey.
As special counsel, Mueller will direct an FBI counterintelligence investigation examining whether Russian Federation coordinated with Trump campaign associates to influence the election in his behalf.
Trump referred to Comey's testimony at a recent Capitol Hill hearing after which the Justice Department ended up having to amend part of his testimony regarding last year's probe of Hillary Clinton's email practices.
Trump categorically denied he asked Comey to drop his probe of Flynn, whom he fired on February 14 for misleading Vice President Mike Pence, about the extent of his conversations past year with Russia's ambassador. "I think the public should have confidence in what's going on".
Multiple news outlets reported Tuesday that prior to ousting Comey, Trump asked him to terminate an investigation into former National Security Advisor Michael Flynn.
First reactions from Congress were mainly positive.
UN says 200000 more expected to flee Iraq's Mosul
While coalition air strikes have aided the advance of Iraqi forces, they have also reportedly caused hundreds of civilian casualties in the city.
Asked about possible obstruction of justice, Republican House of Representatives Speaker Paul Ryan told reporters the special counsel would "follow the facts where ever they may lead" and that "it is premature to prejudge anything at this point".
The White House says an investigation will prove there was no collusion. "Impeccable credentials. Should be widely accepted".
And not a moment too soon, Democrats said.
In a brief statement he said: "I accept this responsibility and will discharge it to the best of my ability".
Trump is leaving Friday for his first foreign trip, to the Mideast and beyond, and aides had hoped the disarray at home would have been calmed if not resolved, allowing the White House to refocus and move ahead. Stocks fell sharply on Wall Street Wednesday as investors anxious the latest turmoil in Washington could hinder Mr Trump's pro-business agenda. During a commencement address Wednesday at the Coast Guard Academy, he complained bitterly about criticism he's faced.
In a statement, Trump said an investigation will confirm that "there was no collusion" between his campaign and Russian Federation. "You can't let the critics and the naysayers get in the way of your dreams". I guess that's why we won.
Trump knows a thing or two about political witch hunts. Donald Trump doesn't belong in the White House.
Senator calls for ejection of Turkish ambassador
It would be beneficial for this person to change", he said, accusing the diplomat of carrying on Obama-administration policies. In April, the US had criticized Turkish airstrikes against Kurdish militants in Syria and Iraq. "This isn't Turkey .
One striking piece of news emerged from Rosenstein's briefing: He told senators that he had already known Comey was getting fired even as he wrote the memo that Trump cited as a significant justification for the Federal Bureau of Investigation director's dismissal.
A defiant Mr Trump used his Twitter account to suggest he is being unfairly treated.
In statement released by the White House on Wednesday evening, the President was measured in his response.
Mr Mueller has been appointed a special counsel to examine Moscow's alleged efforts to influence last year's United States election.
His advice to the president: "Stay disciplined, stay focused and deliver on the world stage".
The New York Times reported on Thursday that Trump called Comey weeks after he took office on January 20 and asked him when federal authorities were going to say Trump was not under investigation.
Trump denies Comey allegations, collusion with Russian Federation
Questions surrounding alleged ties to Russian Federation have dogged Mr Trump since before his election. Despite knowing of the investigation, Trump appointed Flynn his first national security adviser.
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