"I do think that the special prosecutor provides a sense of calm and confidence perhaps for the American people, which is incredibly important," said Sen. Tim Scott, R-S.C.
Trump strongly disagreed. The appointment, he said "hurts our country terribly." He said it "shows we're a divided, mixed-up, not unified country" and is "a very, very negative thing."
He leapt to make the point again at a joint news conference with President Juan Manuel Santos of Colombia, describing the development as a distraction.
"Well I respect the move, but the entire thing has been a witch hunt," he said, insisting there had been "no collusion" between his campaign and Russia. "I'm fine with whatever people want to do. But we have to go back to running this country really, really well."
The Justice Department announced Wednesday that Mueller has been given sweeping power to investigate Russian interference in the 2016 presidential campaign, including potential links between Moscow and Trump campaign associates.
Despite initially opposing the appointment of an independent counsel, House Speaker Paul Ryan said Thursday that the development "helps assure people and the Justice Department that they're going to go do their jobs independently and thoroughly, which is what we've called for all along."
But Trump, after issuing a measured statement when the news first broke Wednesday evening, allowed his resentment to burst forth Thursday in angry morning tweets.
"This is the single greatest witch hunt of a politician in American history!" Trump wrote, ignoring impeachment efforts and blistering verbal attacks on previous presidents and other political leaders.
"With all of the illegal acts that took place in the Clinton campaign and Obama administration, there was never a special counsel appointed!" he added later, without providing examples.
Trump is leaving Friday for his first foreign trip, to the Mideast and beyond, which aides hope can have the effect of refocusing a White House in disarray.
The president's tweets and comments to the TV anchors drew little reaction from fellow Republicans, who instead joined Democrats in heaping praise on Mueller, a longtime respected law officer who served under Presidents George W. Bush and Barack Obama, preceding Comey as head of the FBI. Now, Mueller will have nearly unfettered access to witnesses and information, and the ability to bring criminal charges.
Despite the appointment, at least three congressional committees are continuing their 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.