Most Republicans did not join their Democratic colleagues in calling for a special prosecutor, preferring to keep their faith in the congressional and career FBI investigators.
His appointment, by Deputy Attorney General Rod Rosenstein, was a striking shift for the Justice Department, which had resisted increasingly insistent calls from Democrats for an outside prosecutor.
That's according to several United States senators who met with Rosenstein Thursday afternoon in a secure room in the Capitol basement.
"This was a very good first step".
"If the president gives his word to the American people or to legislatures or to a foreign power, then everyone on every level has to know that he means what he says, and he says what he means", said Rick Tyler, former adviser to Ted Cruz's presidential campaign and former spokesman for Newt Gingrich.
Asked about the potential that there had been obstruction of justice, Republican House of Representatives Speaker Paul Ryan told reporters the special counsel will "follow the facts where ever they may lead" and that "it is premature to prejudge anything at this point".
"This is the single greatest witch hunt of a politician in American history!". He did not provide examples or evidence of any alleged "illegal acts". "If there has to be a special counsel, they made an excellent choice", said Rep. Peter King, a Republican from NY. And President Richard Nixon resigned after a damning investigation by a select committee, before he could be impeached.
Rosenstein did not notify White House Counsel Donald McGahn of Mueller's appointment until Justice Department officials were already briefing reporters, the Post notes.
Trump sent shockwaves across Washington last week by unceremoniously sacking his FBI director - a virtually unprecedented move that came as James Comey was heading an investigation into Team Trump's links to Russian Federation.More news: Paul Pogba to return for Manchester United vs Crystal Palace
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In appointing Mueller, the Justice Department selected a seasoned law enforcement veteran who guided the Federal Bureau of Investigation through the aftermath of the September 11 attacks and led its terror-fighting efforts over the next decade.
He was so valued that former president Barack Obama asked him to stay on two years longer than his 10-year term.
Mr Trump has in vain tried to put investigations into his campaign and his first four months in office behind him.
Rosenstein had faced criticism as the author of a memo that preceded Comey's firing. Friends and former colleagues say it's been tough to see him in such a hard spot, especially when they consider him to be upright, impartial and an unlikely political pawn. Trump later said he had already made a decision to dismiss him and was thinking of "this Russian Federation thing".
"Rod was very cautions about answering any of those questions because he said it is possible for the very creation of that Rosenstein memo to be a part of [newly named special prosecutor Robert Mueller's] investigation".
Reactions from Congress to Mueller's appointment were mainly positive, even though Republicans had dismissed an independent outside investigation as unnecessary and duplicative of what congressional committees already are doing.
At the same time, congressional committees are continuing their own investigations, leading to some turf warfare and sniping as the Senate Intelligence Committee and the Senate Judiciary Committee both sought to lay claim to testimony from Comey, while the House Oversight Committee also hoped to hear from the former director.
Trump strongly disagreed. The appointment, he said in a briefing with news anchors, "hurts our country terribly".
The Russia matter has consumed Washington and overshadowed Republican legislative priorities including a planned healthcare overhaul and sweeping tax cuts, something the party had hoped to make rapid progress on given its control of the White House and both chambers of Congress. "And then on top of that, after the Wednesday performance by Director Comey, you had a person come and have to readjust the record, which many people have never seen before, because there were misstatements made".