He then called the Russian Federation investigation "the single greatest witch hunt in American political history".
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.
The special counsel is also authorised to prosecute any crimes unearthed by the investigation.
Burr, chairman of the Senate panel, said of Flynn and his refusal to comply, "We'll figure out on Gen. Flynn what the next step, if any, is". Flynn, through his lawyer, had earlier asked for immunity from "unfair prosecution" in exchange for agreeing to cooperate with the committee.
The broad federal probe under Mueller, a lawman who engenders deep bipartisan respect, was just getting underway.
Deputy Attorney General Rod Rosenstein on Wednesday tapped Robert Mueller - a widely-respected figure who headed the Federal Bureau of Investigation for the decade after the 9/11 attacks - to take over the FBI's probe of "Russian Government efforts to influence the 2016 presidential election and related matters".
Rosenstein, who at his confirmation hearing would not commit to a special counsel appointment and who inherited the probe following Sessions' recusal, seemed to acknowledge the public outcry by calling Mueller's selection "necessary in order for the American people to have full confidence in the outcome".
"This was a very good first step".
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".
President Donald Trump said Thursday he thinks the appointment of special counsel for the Russian Federation investigation is bad for the United States.
In a statement released by the White House, Trump said: "As I have stated many times, a thorough investigation will confirm what we already know there was no collusion between my campaign and any foreign entity. I look forward to this matter concluding quickly".
But he expressed more resentment Thursday in his tweets.
In another tweet Thursday morning, he claims, "With all of the illegal acts that took place in the Clinton campaign & Obama Administration, there was never a special councel (sic) appointed!"
The US president stands accused of seeking to stall the politically-explosive probe following his shock dismissal of FBI chief James Comey, and allegations that he asked Comey to drop his investigation of a former aide.
This was one of several interactions that Comey believed jeopardized the FBI's independence, the Times reports, and he instructed the president on the proper way to receive details about investigations: have the White House counsel send inquiries to the Department of Justice.
Mueller, a former federal prosecutor at the Justice Department, was confirmed as FBI director days before the September 11, 2001, attacks that would ultimately shape his tenure. That appointment was made by Comey, then the deputy attorney general.
He is empowered to examine "any links and/or coordination between the Russian Government and individuals associated with the campaign of President Donald Trump", Rosenstein's order says.
Republican Sen. Richard Burr of North Carolina says ousted National Security Adviser Flynn's attorneys "have not yet indicated their intentions regarding the Senate Intelligence Committee's subpoena" as part of the panel's probe into Russia's meddling in the 2016 presidential election.