(AP Photo/J. Scott Applewhite).
The committee said Thursday it sent a letter requesting material from the FBI and Justice Department related to its ongoing counterintelligence investigation.
The explosive report sparked calls for the President to be impeached.
Mueller was named as special counsel on Wednesday, one day after a report surfaced that Trump had requested ex-FBI Director James Comey end any investigations involving National Security Adviser Michael Flynn's contacts with Russian Federation.
As special counsel, Mueller is "authorized to prosecute federal crimes arising from the investigation of these matters", according to the Justice Department order Deputy Attorney General Rod Rosenstein signed.
"The special prosecutor will do his job and we'll see where it goes", he said. "I think the public should have confidence in what's going on".
Trump strongly disagreed. The appointment, he said in a briefing with news anchors, "hurts our country terribly".
"And we have very important things to be doing right now, whether it's trade deals, whether it's military, whether it's stopping nuclear - all of the things that we discussed today".
In what appeared to be an abrupt decision, Deputy Attorney General Rod Rosenstein chose Mueller to investigate alleged Russian interference in USA elections previous year as well as "any links and/or coordination between the Russian government and individuals associated with the campaign of President Donald Trump".
Mr Mueller has been appointed a special counsel to examine Moscow's alleged efforts to influence last year's U.S. election.
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!" added Trump. Trump wrote on Thursday morning.
US President Donald Trump has denied all allegations that he tried to pressure fired FBI Director James Comey into dropping a Russia-related probe, and called the appointment of a special counsel to probe claims of his collusion with Russian Federation a "witch hunt".
The latest development came during a week in which the White House faced a series of fresh controversies.
Now, it seems the president has good reason to be nervous since the man appointed for the job is Robert S. Mueller III, an Federal Bureau of Investigation veteran who is respected by both Republicans and Democrats.
Mr Mueller's appointment by the Justice Department a day earlier had dramatically raised the legal and political stakes in an affair that has threatened to engulf the four-month-old presidency.
"This was a very good first step". Leadership is one thing that does trickle down.
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".
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.
The White House says an investigation will prove there was no collusion. This position isn't as powerful as an independent counsel but Mueller will be able to investigate better than Congress can. But GOP lawmakers have grown increasingly anxious since Trump fired Comey, who had been leading the bureau's probe - and after Comey associates said he had notes from a meeting in which Trump asked him to shut down the investigation into the Russian Federation ties of former National Security Adviser Michael Flynn.
A lawyer for fired National Security Adviser Michael Flynn has informed the Senate Intelligence Committee he will not honor its subpoena for private documents. It was not clear what caused the mix-up.