President Donald Trump declared himself the victim of the "greatest witch hunt" in American political history Thursday, lashing out after a probe into his campaign ties with Russia was significantly strengthened.

On Wednesday, a high-powered special counsel was appointed to investigate events around the 2016 election -- a move that left the Republican billionaire seething, and sent world stock markets tumbling.

Hours after former FBI director Robert Mueller was tapped to take over the investigation, Trump took to Twitter in the early morning to scrub the White House's earlier, more measured, response.

"This is the single greatest witch hunt of a politician in American history!" Trump wrote, his anger bubbling over.

"With all of the illegal acts that took place in the Clinton campaign & Obama Administration, there was never a special counsel appointed!" he said, without providing evidence for those claims.

Trump has repeatedly denied any collusion between his campaign and the Kremlin, amid accusations from US intelligence that Russian President Vladimir Putin orchestrated a sweeping campaign to tilt the vote in the Republican's favor.

At the center of the political firestorm are Trump's former national security advisor Michael Flynn and his one-time campaign manager Paul Manafort, and their multiple undisclosed contacts with Russian officials during and after the vote.

So far, no evidence of collusion has been presented, but the question has consumed the first four months of Trump's presidency and spurred multiple crises that have left the White House shell-shocked.

- Crisis after crisis -

Trump sent shockwaves across Washington last week by unceremoniously sacking his FBI director -- a virtually unprecedented move that came as James Comey was heading an investigation into Team Trump's links to Russia.

It later emerged that Comey had made notes of his meetings with Trump, who reportedly asked him to quash an investigation into Flynn's contacts with foreign governments.

Trump was then accused of divulging highly sensitive classified information gleaned by Israeli spies to visiting Russian Foreign Minister Sergei Lavrov.

The triple whammy has left Trump aides dazed and wondering about the future of his young presidency.

With Trump only 8% of the way through its term, his advisors spend their days swapping rumors of mass White House firings.

Others are already considering leaving, and allies due to join the administration say they are holding off.

The appointment of Mueller as special counsel will raise the intensity of the investigation and make it less vulnerable to political interference.

Fighting back has consumed much of the political oxygen inside the White House, leaving Trump's agenda in doubt.

But the president's most powerful ally on Capitol Hill, House Speaker Paul Ryan, on Thursday said the work of government would continue regardless.

"It's always nice to have less drama," he said. "That doesn't seize up Congress. That doesn't stop us from doing our jobs to work on people's problems."

Some of Trump's Republican allies, such as Congressman Jason Amash, have begun cautiously suggesting impeachment is no longer impossible.

With the 2018 Congressional mid-term elections fast approaching, maybe of Trump's erstwhile allies face a difficult campaign dominated by questions about the president's conduct and with few legislative victories to fall back on.

A Gallup tracking poll put Trump's approval rating at a historically low 38%, even before the latest wave of scandals.