The move followed a week in which the White House was thrown into an uproar amid rising demands by Democrats and some of Trump’s fellow Republicans for an independent probe of whether Russia tried to sway the outcome of November’s presidential election in favour of Trump and against Democrat Hillary Clinton.

In a statement after the Justice Department announcement on Wednesday, Trump said he looked forward to a quick resolution of the matter.

“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,” he said.

Mueller, in a statement tweeted by CBS News said: “I accept this responsibility and will discharge it to the best of my ability.”

Trump has long bristled at the notion that Russia played any role in his November election victory, but the Russia issue has clouded his early months in office. Moscow has denied US intelligence agencies’ conclusion it meddled in the campaign.

But pressure on the White House intensified after Trump’s firing last week of Federal Bureau of Investigation chief James Comey, who had been leading a federal probe into the matter, and allegations that Trump had asked Comey to end the FBI investigation.

The issue spilled over onto Wall Street on Wednesday where the S&P 500 and the Dow had their biggest one-day declines since September as investor hopes for tax cuts and other pro-business policies faded amid the political tumult.

“My decision (to appoint a special counsel) is not the finding that crimes have been committed or that any prosecution is warranted. I have made no such determination,” Deputy Attorney General Rod Rosenstein said in a statement announcing the special counsel.

“I determined that a special counsel is necessary in order for the American people to have full confidence in the outcome,” he said.

Lawmakers on Capitol Hill welcomed the Justice Department action, but House and Senate Republican leaders said they would go on with their own investigations of the Russia matter.

Senate Democratic leader Chuck Schumer said Mueller was the right choice for the job.

“A special counsel is very much needed in this situation and Deputy Attorney General Rosenstein has done the right thing,” Schumer said in a statement.

Republican House Judiciary Committee Chairman Bob Goodlatte said he was confident Mueller “will conduct a thorough and fair investigation.”

Mueller, 72, was decorated as a Marine Corps officer during the Vietnam War.

A former federal prosecutor, he is known for his tough, no-nonsense managerial style.

Appointed by Republican President George W Bush, he became FBI director one week before the September 11, 2001, attacks.

In 2011, he was asked by Democratic President Barack Obama for two more years. He was replaced by Comey in 2013.

Some past independent investigations have stretched for years.

For example, Kenneth Starr, who investigated former President Bill Clinton, probed allegations surrounding his past real estate deals but later expanded the inquiry into Clinton’s relations with then-White House intern Monica Lewinsky, leading to an impeachment of Clinton by the House.

Meanwhile, Trump has told graduates of the US Coast Guard Academy that no other politician has been treated more unfairly by the media. But he says, “you cannot let them get you down.”

“Look at the way I’ve been treated lately, especially by the media,” he said. “No politician in history, and I say this with great surety, has been treated worse or more unfairly.”

Trump was offering his advice at the academy’s commencement in Connecticut, telling the graduates that they will find that “things are not always fair.” But, he added, “you have to put your head down and fight, fight, fight.”

The president says they can’t let the critics get in the way of their dreams.

– Reuters/AAP