"Public trust is on the line and the country deserves answers sooner rather than later", he said, adding that Congress needs "all of the facts surrounding the firing of FBI Director Comey".
Meanwhile, House Democratic leader Nancy Pelosi is urging Democrats to sign a discharge petition to establish an independent commission to investigate Russian interference in the presidential election and whether associates of the president co-operated with that effort.
"My decision [to appoint a special counsel] is not the finding that crimes have been committed or that any prosecution is warranted".
Deputy Attorney General Rod Rosenstein said he made this decision out of the enormous "public interest" in this investigation.
Special counsels are appointed to avoid potential conflicts of interest in Justice Department investigations.
The White House maintains that the memo is not an accurate portrayal of the conversation between Mr Trump and Mr Comey. Those calls grew louder as a number of bombshell news reports emerged raising questions about Trump's dealings with Russian Federation and Comey.
NKorea vows to strengthen nukes as US increases pressure
At the Pentagon, Defense Secretary Jim Mattis said the missile test showed North Korea isn't heeding cautions from the worldwide community.
And then there was the story that he had tried to stop the FBI investigation into his former national security adviser.
Mueller was Comey's immediate predecessor at the Federal Bureau of Investigation, which he led from 2001 to 2013 under both George W. Bush and Barack Obama.
Multiple government bodies have been conducting inquiries into Russia's meddling in the 2016 U.S. presidential election and potential instances of collusion between the Kremlin and Trump associates.
Comey was abruptly fired May 9 and learned of the dismissal as he was giving a talk in Los Angeles.
Spicer was also asked about those saying Trump current scandal is of Watergate proportions, and also about Vladimir Putin's offer to release a transcript of what Trump told Foreign Minister Sergey Lavrov at the White House last week.
"A criminal case would require proving that Trump acted corruptly with the specific intent of interfering with the investigation" the attorneys write on Lawfare Blog.
Deputy AG Rosenstein 'frustratingly cautious' in House briefing
Asked if Mueller's appointment would preempt his own request for Comey information, the Iowa Republican replied, "I don't know". Hurd also disagreed with the President's comments on Thursday that the appointment of a special counsel "hurts our country".
Allegations that Trump interfered with an FBI investigation stemmed from a New York Times report Tuesday that Comey had documentation of a February conversation between him and Trump in which the president urged Comey to discontinue the investigation of Flynn.
"Israel has full confidence in our intelligence-sharing relationship with the United States and looks forward to deepening that relationship in the years ahead under President Trump", said Israel's ambassador to the US, Ron Dermer.
Two Democrats in the House of Representatives, Maxine Waters and Al Green, have called for articles of impeachment to be drawn up, but most lawmakers are holding fire, fearing it could transform the process into a purely partisan exercise.
Lawmakers on Capitol Hill generally welcomed the Justice Department action and praised Mr. Mueller for his integrity, but House and Senate Republican leaders said they would go on with their own investigations of the Russian Federation matter.
"We must continue to follow the facts wherever they lead so that we can get to the bottom of this", he said.
The Department of Justice working under Trump is unlikely to prosecute the president, but Congress can classify an obstruction of justice as a high crime, or impeachable offense.
Ana Navarro Calls Out GOP: You'd Impeach Hillary Clinton Over This
In 2013, he lashed out at Edward Snowden, the National Security Agency worker who leaked USA government surveillance documents. The FBI has been investigating possible ties between Trump's campaign and Russian Federation during the election.